demand-of-your-art.jl

### A Pluto.jl notebook ###
# v0.19.25

using Markdown
using InteractiveUtils

# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
    quote
        local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
        local el = $(esc(element))
        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
        el
    end
end

# ╔═╡ d9e64c42-cef6-444d-a5e4-d266488bbd08
using PrettyTables, JuMP, Cbc, PlutoUI, Plots, LinearAlgebra, StatsPlots, Ipopt, SCIP

# ╔═╡ 1a8ed181-8119-4f49-812a-5bcfc3151722
using LaTeXStrings

# ╔═╡ 12385e30-d544-4fd8-aab9-7f6fadfb5ccd
md"""
# Demand of your art

As we saw on [last episode](https://www.youtube.com/watch?v=IOUi1juD5HQ), Javier is creating and selling his art on the beach.
However, we assumed that everything that Javier builds will be sold, which is unrealistic.

Now, we have to deal with a more realistic scenario, in which the demand for Javier's product is not infinite.
We will still need assumptions, but the model is a bit more realistic.
"""

# ╔═╡ c775b393-844e-42a4-9a18-add5dc3ce911
md"""
## Strategy 1: Sell excess inventory at a discount

The first strategy is simple.
If there is no more demand for the products, Javier sells them at a discounted price.

For that, we need to assume that

- Javier knows the demand for each of their products under the price that he decided to sell them;
- Javier discounted price is low enough to sell all of the remaining products.

Below you can see the data.
Notice the new columns **discounted price** and **demand**.
"""

# ╔═╡ 4b1f59f4-1ad3-4bb8-8fc5-ba0578fd4de6
begin
	materials = ["beads", "string", "wire"]
	products = ["bracelet", "necklace", "earring"]

	material_per_product = [
		15 0.6 0.15;
		80 2.5 0.2;
		4 0.1 0.15;
	]
	selling_price = [25.0; 45.0; 10]
	discounted_selling_price = [8.0; 30.0; 3.5]
	hours_to_assemble = [2.5; 4; 1.5]
	demand = [4, 2, 3]
	
	units = " (" .* ["u", "m", "m", "€", "€", "h", "u"] .* ")"

	pretty_table(
		HTML,
		[material_per_product selling_price discounted_selling_price hours_to_assemble demand],
		header=[materials; "price"; "discounted price"; "hours"; "demand"] .* units,
		row_labels=products,
	)
end

# ╔═╡ d00174ed-45d7-4a1b-8b5a-4c4c22e2045a
begin
	material_cost = [0.25; 0.70; 1.5]
	pretty_table(
		HTML,
		material_cost',
		header=materials .* units[1:3],
		row_labels=["cost (€)"],
	)
end

# ╔═╡ c44623d4-b378-4250-bd6a-20d5525ad315
md"""
## Modeling

Our new model is pretty much the same as before, but I will bring the new parts to your attention.

### How to model discounted price

(see also piece-wise concave linear objective)

Let's consider only the bracelet: selling price €25 up to 4 units and €8 after that.

One way of describing our objective is by defining the nonlinear function $\text{revenue}(q)$:
"""

# ╔═╡ e1c97f9e-4504-4265-97df-c340ff955666
md"""
$\text{revenue}(q) = \left\{\begin{array}{cc}
25q, & 0 \leq q \leq 4, \\
25\times 4 + (q - 4)\times 8, & q > 4.
\end{array}\right.$
"""

# ╔═╡ f4bfb073-e33d-4cb1-957b-f90df7d9d8ad
let
	c1 = selling_price[1]
	c2 = discounted_selling_price[1]
	x1 = demand[1]
	x2 = 10
	plot(
		[0, x1, x2],
		[0, c1 * x1, c1 * x1 + (x2 - x1) * c2],
		lab = "",
		m = (2,:lightblue),
	)
	xlabel!("Quantity")
	ylabel!("Revenue")
	png("revenue-function")
	plot!()
end

# ╔═╡ cdec7db4-75db-4009-86e8-695c9dc1a6c3
md"""
This is not linear, though, so to maximize this function we need to some modeling magic, and in this case there is a very simple approach.

First, we split the quantity decision variable $q$ into two parts:

- Quantity under demand: $\underline{q}$
- Quantity over demand: $\overline{q}$

Then, the revenue function can be expressed as

$25\underline{q} + 8\overline{q} \quad \text{subject to} \quad \underline{q} \leq 4, \ \overline{q} \geq 0$

And whenever cost is not important, use $\underline{q} + \overline{q}$ instead of $q$.
We can, to improve readability, create that as an expression $q = \underline{q} + \overline{q}$.

It might not be clear at first why this works, since $q = \underline{q} + \overline{q}$ does not imply that we are selling **first** the normal priced items.
The reason that it works is that we are maximizing the revenue.
This means that if you have to write $7 = \underline{q} + \overline{q}$ to maximize revenue, one would prefer $\underline{q} = 4$ and $\overline{q} = 3$.

Notice that the new constraints $\underline{q} \leq 4$ and $\overline{q} \geq 0$ are necessary.
"""

# ╔═╡ e8d3422f-4720-4c9c-ad2b-9fc1a96fc63f
md"""
production = $(@bind ui_prod3d Slider(0:8, show_value=true)) $br
θ, ϕ = $(@bind ui_θ Slider(0:5:90, default=20)), $(@bind ui_ϕ Slider(0:5:90, default=20))
"""

# ╔═╡ 6eaab6b8-7541-44db-bab6-632009145a0a
let
	prod = ui_prod3d
	c1 = selling_price[1]
	c2 = discounted_selling_price[1]
	x1 = demand[1]
	x2 = 10
	plt = plot(layout=grid(1, 2), size=(800, 500))
	f(x, y) = c1 * x + c2 * y
	contourf!(
		plt[1],
		range(0, x1, length=5),
		range(0, x2 - x1, length=5),
		f,
		lab = "",
		lw=0.2,
		m = (2,:lightblue),
		axis_ratio = :equal,
	)
	surface!(
		plt[2],
		range(0, x1, length=5),
		range(0, x2 - x1, length=5),
		f,
		lab = "",
		m = (2,:lightblue),
		camera = (ui_θ, ui_ϕ),
		colorbar = false,
	)
	X = min.(x1, prod:-1:0)
	Y = 0:prod
	Z = f.(X, Y)
	plot!(plt[1], X, Y, c=:lightblue, lab="", m=(3,:lightblue,stroke(1,:blue)))
	plot!(plt[2], X, Y, Z, c=:lightblue, lab="", m=(3,:lightblue,stroke(1,:blue)))
	# end
	xlims!(-0.2, x1 + 0.2)
	ylims!(-0.2, x2 - x1 + 0.2)
	zlims!(plt[2], -0.2, f(x1, x2 - x1) + 0.2)
	xlabel!(plt[1], "Normal production")
	ylabel!(plt[1], "Extra production")
end

# ╔═╡ 690b0069-f041-462c-b564-638506ff2346
md"""
### Model

**Sets**:

- Products: $p \in \mathcal{P}$
- Materials: $m \in \mathcal{M}$
"""

# ╔═╡ 3e0cfd88-0848-4555-943d-0a8e716b1928
md"""
**Parameters**:

| Name | Unit | Identifier | Set |
|:--|:--|:--|:--|
| Time availability | h | $\text{time\_available}$ | |
| Selling price of $p$ | € / unit | $\text{selling\_price}_p$ | $p \in \mathcal{P}$ |
| **(New) Discounted price of $p$** | € / unit | $\text{discounted\_selling\_price}_p$ | $p \in \mathcal{P}$ |
| **(New) Demand for product $p$** | unit | $\text{demand}_p$ | $p \in \mathcal{P}$ |
| Hours to assemble product $p$ | $h$ / unit | $\text{assemble\_time}_{p}$ | $p \in \mathcal{P}$ |
| Material $m$ cost | € / [$m$] | $\text{material\_cost}_m$ | $m \in \mathcal{M}$ |
| Amount of $m$ per unit of $p$ | [$m$] / unit | $\text{mat\_per\_prod}_{p,m}$ | $p \in \mathcal{P}, m \in \mathcal{M}$ |
"""

# ╔═╡ 5fca3abb-6ace-4ee3-b8a3-ae3d40355493
md"""
**Variables**:

As mentioned, the production variable is split into two parts, one to possibly satisfy the demand, and one for extra products sold.

- Amount of product $p$ assembled and sold at full price (unit): $\text{prod\_normal}_p, \quad p \in \mathcal{P}$
- Amount of product $p$ assembled and sold at discount (unit): $\text{prod\_extra}_{p}, \quad p \in \mathcal{P}$
"""

# ╔═╡ 5112c1c4-4ade-47eb-b17d-ddfee5ceb923
md"""
**Expressions**:

As mentioned before, let's create a helper expression for the total amount of products produced.
This essentially allows us to reuse all other expressions and constraints.

- Amount produced and sold of product $p$:
$\displaystyle \text{prod}_p = \text{prod\_normal}_{p} + \text{prod\_extra}_{p}, \quad p \in \mathcal{P}$
- Revenue:
$\begin{align}
\text{revenue} = & \sum_{p \in \mathcal{P}} \bigg( \text{selling\_price}_p \times \text{prod\_normal}_{p} + \\
& \text{discounted\_selling\_price}_p \times \text{prod\_extra}_{p}
\bigg)
\end{align}$
- Total Used Material:
$\displaystyle \text{total\_used\_material}_m = \sum_{p \in \mathcal{P}} \text{mat\_per\_prod}_{p,m} \times \text{prod}_p, \quad m \in \mathcal{M}$
- Total Material Cost:
$\displaystyle \text{total\_material\_cost} = \sum_{m \in \mathcal{M}} \text{total\_used\_mat}_m \times \text{material\_cost}_m, \quad m \in \mathcal{M}$
- Time expenditure:
$\text{time\_spent} = \displaystyle \sum_{p \in \mathcal{P}} \text{assemble\_time}_{p} \times \text{prod}_p$
"""

# ╔═╡ 74b99316-b892-4682-affd-b6f060e976dd
md"""
**Objective**:

- Maximize profit:
$\text{maximize} \quad \text{revenue} - \text{total\_material\_cost}$
"""

# ╔═╡ 22e49663-e352-4b18-b4eb-04f04d8eb99b
md"""
**Constraints**:

Now, to finalize, we have the extra constraints mentioned before.

- Production under demand:
$\text{prod\_normal}_{p} \leq \text{demand}_p, \quad p \in \mathcal{P}$
- Nonnegativity:
$\text{prod\_normal}_{p}, \ \text{prod\_extra}_{p} \geq 0$
- Integer production:
$\text{prod\_normal}_{p}, \ \text{prod\_extra}_{p} \in \mathbb{Z}$
- Time Availability:
$\text{spent\_time} \leq \text{time\_available}$
"""

# ╔═╡ 9c6136a1-e603-47c1-9df6-2445fcba3933
begin
	# using JuMP, Cbc
	function optimize_production(time_availability)
		model = Model(Cbc.Optimizer)
		set_attribute(model, "logLevel", 0)

		num_products = length(products)
		num_materials = length(materials)

		@variable(model,
			0 ≤ prod_normal[p=1:num_products] ≤ demand[p],
			Int
		)
		@variable(model,
			prod_extra[p=1:num_products] ≥ 0,
			Int
		)

		prod = prod_normal + prod_extra

		@expression(model,
			total_used_material[m=1:num_materials],
			sum(
				material_per_product[p, m] * prod[p]
				for p in 1:num_products
			)
		)

		total_mat_cost = sum(total_used_material .* material_cost)
		revenue = sum(prod_normal .* selling_price + prod_extra .* discounted_selling_price)

		profit = revenue - total_mat_cost
		time_expenditure = sum(hours_to_assemble .* prod)

		@objective(model, Max, profit)

		@constraint(model, time_expenditure ≤ time_availability)

		optimize!(model)

		return Dict(
			:prod_normal => value.(prod_normal),
			:prod_extra => value.(prod_extra),
			:objective => objective_value(model),
			:model => model,
			:revenue => value(revenue),
			:profit => value(profit),
		)
	end
end

# ╔═╡ ea2a69b8-c883-444e-b09b-9890c551c64d
md"""
Time Availability = $(@bind slider_time_availability Slider(0:40, show_value=true))
"""

# ╔═╡ bad1999d-c085-433c-a42e-d309ae2ae624
let
	output = optimize_production(slider_time_availability)
	prod_normal = output[:prod_normal]
	prod_extra = output[:prod_extra]
	pretty_table(
		HTML,
		[prod_normal prod_extra],
		row_labels=products,
		header=["normal production"; "extra production"],
	)
end

# ╔═╡ f99652cb-bc7e-4400-98bd-3373de0e978b
let
	output = optimize_production(slider_time_availability)
	prod_normal = output[:prod_normal]
	prod_extra = output[:prod_extra]
	groupedbar(
		hcat(sum.([prod_extra, prod_normal], dims=2)...),
        bar_position = :stack,
        bar_width = 0.5,
        xticks = (1:length(products), string.(products)),
		label = ["extra" "normal"],
	)
	ylims!(0, 7)
end

# ╔═╡ 6991aec5-0d20-4ef3-a85a-668fb2a24334
let
	profits = Float64[]
	slacks = Float64[]
	for time_availability = 0:40
		output = optimize_production(time_availability)
		push!(profits, output[:profit])
	end

	plt = plot(size=(600, 600))
	plot!(
		plt,
		profits,
		lab="profits",
		m=(3, :lightblue, stroke(1, :blue)),
		c=:blue,
	)
	xlabel!("Time availability")
	ylabel!("€")
	png("revenue-strategy1")
	plot!()
end

# ╔═╡ af603777-9d1b-4382-b62f-5d997211c500
md"""
## Strategy 2: Demand is a function of price

Our second approach is to consider that the demand for the products depends on their price and to add this relation into the model.
In other words, we are not only deciding how many products we will build, we will decide at which price we will sell them.

To do that we have to assume that we know how the demand depends on the price, which is not something trivial to figure out.
For today, let's assume that this dependency will be linear:

$\text{demand} = \text{intercept} + \text{slope} \times \text{price},$

and that we now the intercept and slope values for each product.
"""

# ╔═╡ 1ef83b37-910c-474f-bc20-0298673ae813
md"""
product = $(@bind selected_product Select([j => p for (j, p) in enumerate(products)]))
"""

# ╔═╡ c9164c4a-d962-463a-a3d1-77958a72968e
md"""
Below are the values that we assume represent the demand.
"""

# ╔═╡ fa7064dd-c06d-469e-b8a5-d71d498f872a
begin
	demand_slope = -[0.5; 0.4; 2.0]
	# L = I + m x = d₀ + m (x - p₀)
	# ⇒ I = d₀ - m p₀
	demand_intercept = demand - demand_slope .* selling_price

	pretty_table(
		HTML,
		[demand_intercept demand_slope],
		row_labels=products,
		header=["demand intercept (unit)", "demand slope (unit / €)"]
	)
end

# ╔═╡ f8c7d28c-ae76-4f29-8f6a-a0492d8c080c
md"""
price = $(@bind price_slider Slider(0:ceil(Int, selling_price[selected_product] - demand[selected_product] / demand_slope[selected_product]), default=selling_price[selected_product], show_value=true))
"""

# ╔═╡ a755c453-cd1e-4b33-bfa2-28e44c1fba0c
let
	d₀ = demand[selected_product]
	p₀ = selling_price[selected_product]
	α = demand_slope[selected_product]
	demand_f(p) = d₀ + (p - p₀) * α
	p_max = (α * p₀ - d₀) / α

	plt = plot(layout=grid(1,2), size=(800,500))
	plot!(plt[1], demand_f, 0, p_max, ylabel="quantity", title="demand", lab="", axis_ratio=:equal)
	p = price_slider
	d = demand_f(p)
	plot!(plt[1], [p, p, 0], [0, d, d], c=:lightblue, l=:dash, fill=true, lab="revenue")
	scatter!(plt[1], [p₀], [d₀], lab="original")
	title!(plt[1], "price of $(products[selected_product])")
	xticks!(plt, 0:5:5 * ceil(Int, p_max / 5))
	xlims!(plt, 0, p_max + 1)
	ylims!(plt[1], 0, d₀ - α * p₀ + 1)
	xlabel!(plt, "price")

	prices = range(0, p_max, length=100)
	demands = prices .* demand_f.(prices)
	plot!(plt[2], prices, demands, lab="revenue")
	plot!(plt[2], [p, p], [0, d * p], c=:lightblue, l=:dash, lab="")
	scatter!(plt[2], [p], [d * p], c=:red, lab="")
	png("demand-given-price$selected_product")
	plot!()
end

# ╔═╡ 9287c22d-6261-4160-97c8-8b00a01ff48c
md"""
### Modeling

There are a few more nuanced differences in this model.

**Sets**:

- Products: $p \in \mathcal{P}$
- Materials: $m \in \mathcal{M}$

**Parameters**:

| Name | Unit | Identifier | Set |
|:--|:--|:--|:--|
| Time availability | h | $\text{time\_available}$ | |
| **(new) Demand of product $p$ (intercept)** | unit | $\text{demand\_intercept}_p$ | $p \in \mathcal{P}$ |
| **(new) Demand of product $p$ (slope)** | unit / [€] | $\text{demand\_slope}_p$ | $p \in \mathcal{P}$ |
| Hours to assemble product $p$ | h / unit | $\text{assemble\_time}_p$ | $p \in \mathcal{P}$ |
| Material $m$ cost | € / [$m$] | $\text{material\_cost}_m$ | $m \in \mathcal{M}$ |
| Amount of $m$ per unit of $p$ | [$m$] / unit | $\text{mat\_per\_prod}_{p,m}$ | $p \in \mathcal{P}, m \in \mathcal{M}$ |
"""

# ╔═╡ 36084aee-33b3-4889-bc73-b98ec1348e13
md"""
**Variables**:

- Amount of product $p$ assembled and sold (unit): $\quad \text{prod}_p, \quad p \in \mathcal{P}$
- **(New) Price of product $p$ (€)**: $\quad \text{decided\_price}_p, \quad p \in \mathcal{P}$
"""

# ╔═╡ a8174177-0764-4936-abb9-fc78d369a792
md"""
**Expressions**:

A few things changed here.
First, the demand is an expression now, which we will use in the constraints.

Second, and maybe most important, the revenue is quadratic now.
This by itself is not an issue, but when coupled with the integrality of the variable $\text{prod}_p$, we have a much harder problem on our hands.

- **(New) Demand**:
$\displaystyle \text{demand\_given\_price}_p = \text{demand\_intercept}_p + \text{demand\_slope}_p \times \text{decided\_price}_p, \quad p \in \mathcal{P}$
- Revenue:
$\displaystyle \text{revenue} = \sum_{p \in \mathcal{P}} \text{decided\_price}_p \times \text{prod}_p$
- Total Used Material:
$\displaystyle \text{total\_used\_material}_m = \sum_{p \in \mathcal{P}} \text{mat\_per\_prod}_{p,m} \times \text{prod}_p, \quad m \in \mathcal{M}$
- Total Material Cost:
$\displaystyle \text{total\_material\_cost} = \sum_{m \in \mathcal{M}} \text{total\_used\_material}_m \times \text{material\_cost}_m$
- Time expenditure:
$\text{time\_spent} = \displaystyle \sum_{p \in \mathcal{P}} \text{assemble\_time}_p \times \text{prod}_p$
"""

# ╔═╡ 6f290571-9518-4300-8b0a-f44b71c267c8
md"""
**Objective**:

- Maximize profit:
$\text{maximize} \quad \text{revenue} - \text{total\_material\_cost}$
"""

# ╔═╡ 22b7f8f1-ffb7-44dd-bb58-e35d32baf9df
md"""
**Constraints**:

The new constraint of the model is relating the production to the price via the demand.
Notice that the actual constraint could be written using equality.
However, since the production is an integer, and the price is a floating-point number, it might be that the actual demand value (which should be an integer), is just a little bit off.
Depending on the solver, it might help a lot.

- **(New) Produce what you can sell**:
$\text{prod}_p \leq \text{demand\_given\_price}_p, \quad p \in \mathcal{P}$
- Time Availability:
$\text{spent\_time} \leq \text{time\_available}$
- Non-negativity:
$\text{prod}_p, \ \text{decided\_price}_p \geq 0, \quad p \in \mathcal{P}$
- Integer production:
$\text{prod}_p \in \mathbb{Z}$
"""

# ╔═╡ b3182f7f-2949-4720-b2b9-c0232e0c133f
md"""
## Implementation

Last time we used the Cbc solver to solve our problem.
It had integer variables, but it was otherwise linear.

This time, the objective is quadratic.
Therefore, we need to use a different solver.
SCIP is a good open-source choice.
"""

# ╔═╡ 4c2d14a6-b074-4c9c-885a-106863336e0f
begin
	# using JuMP, SCIP
	function optimize_production_nonlinear(time_availability)
		model = Model(SCIP.Optimizer)
		set_attribute(model, "display/verblevel", 0)
		set_attribute(model, "limits/gap", 0.01)

		num_products = length(products)
		num_materials = length(materials)
		
		@variable(model,
			prod[p=1:num_products] ≥ 0, Int
		)
		@variable(model,
			decided_price[p=1:num_products] ≥ 0,
		)

		demand_given_price = demand_intercept + demand_slope .* decided_price
	
		@expression(model,
			total_used_material[m=1:num_materials],
			sum(
				material_per_product[p, m] * prod[p]
				for p in 1:num_products
			)
		)

		total_mat_cost = sum(total_used_material .* material_cost)
		revenue = sum(
			prod[p] * decided_price[p]
			for p in 1:num_products
		)
		
		profit = revenue - total_mat_cost
		time_expenditure = sum(hours_to_assemble .* prod)
	
		@objective(model, Max, profit)
	
		@constraint(model, time_expenditure .≤ time_availability)
		@constraint(model,
			production_limited_by_demand[p=1:num_products],
			prod[p] ≤ demand_given_price[p],
		)
	
		optimize!(model)
	
		return Dict(
			:prod => value.(prod),
			:demand => value.(demand_given_price),
			:price => value.(decided_price),
			:objective => objective_value(model),
			:model => model,
			:revenue => value(revenue),
			:profit => value(profit),
		)
	end
end

# ╔═╡ 65604aec-a34d-45e2-a8f2-92a25d91276d
md"""
## Results
"""

# ╔═╡ 7b68ff21-3ba1-4041-a5a9-ad521624a546
md"""
time availability = $(@bind slider_time_availability2 Slider(0:40, show_value=true))
"""

# ╔═╡ 3f0ed7cd-39b6-41a6-8702-95a0fb237065
let
	output = optimize_production_nonlinear(slider_time_availability2)
	prod = output[:prod]
	demand = output[:demand]
	price = output[:price]
	product_labels = [
		products[i] * " $(round(price[i], digits=2))"
		for i = 1:3
	]
	bar(
		(1:3) .- 0.2,
		prod,
        bar_position = :stack,
        bar_width = 0.4,
        xticks = (1:length(products), product_labels),
		label="production",
	)
	bar!(
		(1:3) .+ 0.2,
		demand,
        bar_position = :stack,
        bar_width = 0.4,
        xticks = (1:length(products), product_labels),
		opacity=0.5,
		label="demand",
	)
	ylims!(0, 7)
end

# ╔═╡ ecf2f51b-4199-48f8-8575-89ce8ce9a4ab
let
	for max_t = [40, 80]
		profits = Float64[]
		slacks = Float64[]
		for time_availability = 0:max_t
			output = optimize_production_nonlinear(time_availability)
			push!(profits, output[:profit])
		end
	
		plt = plot(size=(600, 600))
		plot!(
			plt,
			0:max_t,
			profits,
			lab="profits",
			m=(3, :lightblue, stroke(1, :blue)),
			c=:blue,
		)
		xlabel!("Time availability")
		ylabel!("€")
		png("revenue-strategy2-$max_t")
	end
	plot!()
end

# ╔═╡ a4e70d13-a1ca-4582-b7b7-3b96d4f9de58
md"""
---
Extras for the blog post
"""

# ╔═╡ e3111d88-3462-47d9-8a7f-8690fe1df371
let
	c1 = selling_price[1]
	c2 = discounted_selling_price[1]
	x1 = demand[1]
	x2 = 10

	anim = @animate for prod = range(0, 10, length=80)
		plt = plot(layout=grid(1, 2), size=(800, 400))
		f(x, y) = c1 * x + c2 * y
		contourf!(
			plt[1],
			range(0, x1, length=5),
			range(0, x2 - x1, length=5),
			f,
			lab = "",
			lw=0.2,
			m = (2,:lightblue),
			axis_ratio = :equal,
		)
		X = min.(x1, prod:-1:0)
		X = [min(prod, x1), min(prod, x1), 0]
		Y = [0, prod - min(prod, x1), prod]
		plot!(plt[1], X, Y, c=:white, lw=2, lab="")
		scatter!(plt[1], [X[2]], [Y[2]], m=(3,:pink,stroke(1,:red)), lab="")
		plot!(plt[1], [0, X[1], X[1]], [0, 0, Y[2]], c=:blue, lw=2, lab="")
		
		xlims!(plt[1], -0.2, x1 + 0.2)
		ylims!(plt[1], -0.2, x2 - x1 + 0.2)
		xlabel!(plt[1], "Normal production")
		ylabel!(plt[1], "Extra production")

		plot!(plt[2],
			[0, x1, x2],
			[0, c1 * x1, c1 * x1 + (x2 - x1) * c2],
			lab = "",
			c=:blue,
			m = (2,:lightblue,stroke(1,:blue)),
		)
		plot!(plt[2],
			[prod, prod],
			[0, f(X[2],Y[2])],
			c=:lightblue,
			lab="",
		)
		scatter!(plt[2], [prod], [f(X[2], Y[2])], m=(3,:pink,stroke(1,:red)), lab="")
		xlabel!("Quantity")
		ylabel!("Revenue")
	end
	gif(anim, "revenue.gif", fps=20)
end

# ╔═╡ 52d44b98-1da3-4f1a-84a0-db1b8241a40e
let
	anim = @animate for t = min.(0:60, 40)
		output = optimize_production(t)
		prod_normal = output[:prod_normal]
		prod_extra = output[:prod_extra]
		groupedbar(
			hcat(sum.([prod_extra, prod_normal], dims=2)...),
	        bar_position = :stack,
	        bar_width = 0.5,
	        xticks = (1:length(products), string.(products)),
			label = ["extra" "normal"],
		)
		title!("Available time: $t h")
		ylims!(0, 7)
	end
	gif(anim, "solution-strategy-1.gif", fps=5)
end

# ╔═╡ 81cc6f5e-c8b7-4e8a-a7d9-36ad501f4b44
let
	anim = @animate for t = min.(0:60, 40)
		output = optimize_production_nonlinear(t)
		prod = output[:prod]
		demand = output[:demand]
		price = output[:price]
		product_labels = [
			products[i] * " $(round(price[i], digits=2))"
			for i = 1:3
		]
		bar(
			(1:3) .- 0.2,
			prod,
	        bar_position = :stack,
	        bar_width = 0.4,
	        xticks = (1:length(products), product_labels),
			label="production",
		)
		bar!(
			(1:3) .+ 0.2,
			demand,
	        bar_position = :stack,
	        bar_width = 0.4,
	        xticks = (1:length(products), product_labels),
			opacity=0.5,
			label="demand",
		)
		title!("Available time: $t h")
		ylims!(0, 7)
	end
	gif(anim, "solution-strategy-2.gif", fps=5)
end

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
Cbc = "9961bab8-2fa3-5c5a-9d89-47fab24efd76"
Ipopt = "b6b21f68-93f8-5de0-b562-5493be1d77c9"
JuMP = "4076af6c-e467-56ae-b986-b466b2749572"
LaTeXStrings = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
PrettyTables = "08abe8d2-0d0c-5749-adfa-8a2ac140af0d"
SCIP = "82193955-e24f-5292-bf16-6f2c5261a85f"
StatsPlots = "f3b207a7-027a-5e70-b257-86293d7955fd"

[compat]
Cbc = "~1.1.1"
Ipopt = "~1.3.0"
JuMP = "~1.11.1"
LaTeXStrings = "~1.3.0"
Plots = "~1.38.12"
PlutoUI = "~0.7.51"
PrettyTables = "~2.2.4"
SCIP = "~0.11.6"
StatsPlots = "~0.15.5"
"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised

julia_version = "1.9.0"
manifest_format = "2.0"
project_hash = "577b82dd4350c9935de5ff59e72d2e3f79a41b06"

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git-tree-sha1 = "6252039f98492252f9e47c312c8ffda0e3b9e78d"
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[[deps.AbstractFFTs]]
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version = "1.3.1"
weakdeps = ["ChainRulesCore"]

    [deps.AbstractFFTs.extensions]
    AbstractFFTsChainRulesCoreExt = "ChainRulesCore"

[[deps.AbstractPlutoDingetjes]]
deps = ["Pkg"]
git-tree-sha1 = "8eaf9f1b4921132a4cff3f36a1d9ba923b14a481"
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version = "1.1.4"

[[deps.Adapt]]
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    [deps.Adapt.extensions]
    AdaptStaticArraysExt = "StaticArrays"

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[[deps.Cairo_jll]]
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git-tree-sha1 = "4b859a208b2397a7a623a03449e4636bdb17bcf2"
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[[deps.Calculus]]
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[[deps.Cbc]]
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[[deps.Cbc_jll]]
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git-tree-sha1 = "1d12b6aa435f30bd5619e0144f4c815c854a91b6"
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version = "200.1000.800+0"

[[deps.Cgl_jll]]
deps = ["Artifacts", "Clp_jll", "CoinUtils_jll", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Osi_jll", "Pkg"]
git-tree-sha1 = "3e53a23c0bf96e8c0115777e351a04d5b0f52529"
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[[deps.ChainRulesCore]]
deps = ["Compat", "LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "e30f2f4e20f7f186dc36529910beaedc60cfa644"
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[[deps.Clp_jll]]
deps = ["Artifacts", "CoinUtils_jll", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "METIS_jll", "MUMPS_seq_jll", "OpenBLAS32_jll", "Osi_jll", "Pkg"]
git-tree-sha1 = "51861cd16c6c4e0018ad401b2afb36e51c7d4bcd"
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[[deps.Clustering]]
deps = ["Distances", "LinearAlgebra", "NearestNeighbors", "Printf", "Random", "SparseArrays", "Statistics", "StatsBase"]
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[[deps.CodecBzip2]]
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[[deps.CoinUtils_jll]]
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    DistributionsDensityInterfaceExt = "DensityInterface"

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uuid = "62fd8b95-f654-4bbd-a8a5-9c27f68ccd50"
version = "0.1.1"

[[deps.Test]]
deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

[[deps.TranscodingStreams]]
deps = ["Random", "Test"]
git-tree-sha1 = "9a6ae7ed916312b41236fcef7e0af564ef934769"
uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
version = "0.9.13"

[[deps.Tricks]]
git-tree-sha1 = "aadb748be58b492045b4f56166b5188aa63ce549"
uuid = "410a4b4d-49e4-4fbc-ab6d-cb71b17b3775"
version = "0.1.7"

[[deps.URIs]]
git-tree-sha1 = "074f993b0ca030848b897beff716d93aca60f06a"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.4.2"

[[deps.UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

[[deps.Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"

[[deps.UnicodeFun]]
deps = ["REPL"]
git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
version = "0.4.1"

[[deps.Unzip]]
git-tree-sha1 = "ca0969166a028236229f63514992fc073799bb78"
uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d"
version = "0.2.0"

[[deps.Wayland_jll]]
deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "ed8d92d9774b077c53e1da50fd81a36af3744c1c"
uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
version = "1.21.0+0"

[[deps.Wayland_protocols_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4528479aa01ee1b3b4cd0e6faef0e04cf16466da"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.25.0+0"

[[deps.Widgets]]
deps = ["Colors", "Dates", "Observables", "OrderedCollections"]
git-tree-sha1 = "fcdae142c1cfc7d89de2d11e08721d0f2f86c98a"
uuid = "cc8bc4a8-27d6-5769-a93b-9d913e69aa62"
version = "0.6.6"

[[deps.WoodburyMatrices]]
deps = ["LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "de67fa59e33ad156a590055375a30b23c40299d3"
uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
version = "0.5.5"

[[deps.XML2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "93c41695bc1c08c46c5899f4fe06d6ead504bb73"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.10.3+0"

[[deps.XSLT_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"]
git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a"
uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
version = "1.1.34+0"

[[deps.Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "5be649d550f3f4b95308bf0183b82e2582876527"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.6.9+4"

[[deps.Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4e490d5c960c314f33885790ed410ff3a94ce67e"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.9+4"

[[deps.Xorg_libXcursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
version = "1.2.0+4"

[[deps.Xorg_libXdmcp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fe47bd2247248125c428978740e18a681372dd4"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.3+4"

[[deps.Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.4+4"

[[deps.Xorg_libXfixes_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
version = "5.0.3+4"

[[deps.Xorg_libXi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
version = "1.7.10+4"

[[deps.Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
version = "1.1.4+4"

[[deps.Xorg_libXrandr_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
version = "1.5.2+4"

[[deps.Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.10+4"

[[deps.Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.0+3"

[[deps.Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.13.0+3"

[[deps.Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "926af861744212db0eb001d9e40b5d16292080b2"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.0+4"

[[deps.Xorg_xcb_util_image_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_keysyms_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_renderutil_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
version = "0.3.9+1"

[[deps.Xorg_xcb_util_wm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.1+1"

[[deps.Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "4bcbf660f6c2e714f87e960a171b119d06ee163b"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.2+4"

[[deps.Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "5c8424f8a67c3f2209646d4425f3d415fee5931d"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.27.0+4"

[[deps.Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.4.0+3"

[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.13+0"

[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "49ce682769cd5de6c72dcf1b94ed7790cd08974c"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.5+0"

[[deps.bliss_jll]]
deps = ["Artifacts", "GMP_jll", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "f8b75e896a326a162a4f6e998990521d8302c810"
uuid = "508c9074-7a14-5c94-9582-3d4bc1871065"
version = "0.77.0+1"

[[deps.boost_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "7a89efe0137720ca82f99e8daa526d23120d0d37"
uuid = "28df3c45-c428-5900-9ff8-a3135698ca75"
version = "1.76.0+1"

[[deps.fzf_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "868e669ccb12ba16eaf50cb2957ee2ff61261c56"
uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09"
version = "0.29.0+0"

[[deps.libaom_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3a2ea60308f0996d26f1e5354e10c24e9ef905d4"
uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
version = "3.4.0+0"

[[deps.libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.1+0"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.7.0+0"

[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.2+0"

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+1"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.48.0+0"

[[deps.oneTBB_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "cefc4c476923c22a025d1124dfd10c5781160cea"
uuid = "1317d2d5-d96f-522e-a858-c73665f53c3e"
version = "2021.8.0+0"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+0"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"

[[deps.xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "9ebfc140cc56e8c2156a15ceac2f0302e327ac0a"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "1.4.1+0"
"""

# ╔═╡ Cell order:
# ╠═d9e64c42-cef6-444d-a5e4-d266488bbd08
# ╟─12385e30-d544-4fd8-aab9-7f6fadfb5ccd
# ╟─c775b393-844e-42a4-9a18-add5dc3ce911
# ╟─4b1f59f4-1ad3-4bb8-8fc5-ba0578fd4de6
# ╟─d00174ed-45d7-4a1b-8b5a-4c4c22e2045a
# ╟─c44623d4-b378-4250-bd6a-20d5525ad315
# ╟─1a8ed181-8119-4f49-812a-5bcfc3151722
# ╟─e1c97f9e-4504-4265-97df-c340ff955666
# ╟─f4bfb073-e33d-4cb1-957b-f90df7d9d8ad
# ╟─cdec7db4-75db-4009-86e8-695c9dc1a6c3
# ╟─e8d3422f-4720-4c9c-ad2b-9fc1a96fc63f
# ╟─6eaab6b8-7541-44db-bab6-632009145a0a
# ╟─690b0069-f041-462c-b564-638506ff2346
# ╟─3e0cfd88-0848-4555-943d-0a8e716b1928
# ╟─5fca3abb-6ace-4ee3-b8a3-ae3d40355493
# ╟─5112c1c4-4ade-47eb-b17d-ddfee5ceb923
# ╟─74b99316-b892-4682-affd-b6f060e976dd
# ╟─22e49663-e352-4b18-b4eb-04f04d8eb99b
# ╟─9c6136a1-e603-47c1-9df6-2445fcba3933
# ╟─ea2a69b8-c883-444e-b09b-9890c551c64d
# ╟─bad1999d-c085-433c-a42e-d309ae2ae624
# ╟─f99652cb-bc7e-4400-98bd-3373de0e978b
# ╠═6991aec5-0d20-4ef3-a85a-668fb2a24334
# ╟─af603777-9d1b-4382-b62f-5d997211c500
# ╟─1ef83b37-910c-474f-bc20-0298673ae813
# ╟─f8c7d28c-ae76-4f29-8f6a-a0492d8c080c
# ╟─a755c453-cd1e-4b33-bfa2-28e44c1fba0c
# ╟─c9164c4a-d962-463a-a3d1-77958a72968e
# ╟─fa7064dd-c06d-469e-b8a5-d71d498f872a
# ╟─9287c22d-6261-4160-97c8-8b00a01ff48c
# ╟─36084aee-33b3-4889-bc73-b98ec1348e13
# ╟─a8174177-0764-4936-abb9-fc78d369a792
# ╟─6f290571-9518-4300-8b0a-f44b71c267c8
# ╟─22b7f8f1-ffb7-44dd-bb58-e35d32baf9df
# ╟─b3182f7f-2949-4720-b2b9-c0232e0c133f
# ╟─4c2d14a6-b074-4c9c-885a-106863336e0f
# ╟─65604aec-a34d-45e2-a8f2-92a25d91276d
# ╟─7b68ff21-3ba1-4041-a5a9-ad521624a546
# ╟─3f0ed7cd-39b6-41a6-8702-95a0fb237065
# ╟─ecf2f51b-4199-48f8-8575-89ce8ce9a4ab
# ╟─a4e70d13-a1ca-4582-b7b7-3b96d4f9de58
# ╟─e3111d88-3462-47d9-8a7f-8690fe1df371
# ╟─52d44b98-1da3-4f1a-84a0-db1b8241a40e
# ╠═81cc6f5e-c8b7-4e8a-a7d9-36ad501f4b44
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002