Bailey Scoville
The objective of this linear programming problem is to find the combination of the five foods that minimizes my weekly food costs while ensuring I ingest the weekly recommended amounts of sodium, energy, protein, vitamin D, calcium, iron, and potassium.
- x1 - Kodiak Cakes® Plant-Based Classic Protein Flapjack & Waffle Mix - $0.79 per serving
- x2 - Kirkland Signature Cheese, Fruit & Nut Snack Packs - $0.85 per serving
- x3 - Trader Joe’s Tortilla Española - $ 0.92 per serving
- x4 - BOOST Original Balanced Nutritional Powder Drink Mix, Very Vanilla - $1.42 per serving
- x5 - Trader Joe’s Indian Fare Madras Lentils - $1.25 per serving
- NOTE - images of nutrition labels are included in the repository
- Objective function: Min Z = (6.29/8)*x1 + (13.59/16)*x2 + (5.49/6)*x3 + (33.99/24)*x4 + (2.49/2)*x5
- Subject to:
- 440x1 + 160x2 + 320x3 + 170x4 + 510x5 + x6 = (5000*7) - maximum sodium (mg)
- 230x1 + 180x2 + 150x3 + 220x4 + 150x5 + x7 = (2000*7) - minimum energy (kcal)
- 14x1 + 8x2 + 5x3 + 10x4 + 7x5 + x8 = (50*7) - minimum protein (g)
- 1x1 + 0.1x2 + 0.2x3 + 6x4 + 0.1x5 + x9 = (20*7) - minimum vitamin D (mcg)
- 24x1 + 150x2 + 30x3 + 260x4 + 40x5 + x10 = (1300*7) - minimum calcium (mg)
- 3x1 + 0.4x2 + 0.8x3 + 3.6x4 + 2.1x5 + x11 = (18*7) - minimum iron (mg)
- 155x1 + 80x2 + 320x3 + 290x4 + 360x5 + x12 = (4700*7) - minimum potassium (mg)
- xi ≥ 0, ∀ i
The linear programming code utilizes the Python PuLP library to minimize the cost function. Python code and output plain text files are included in the repository.
The optimal solution includes only two of the five foods: Tortilla Española (x3) and BOOST Drink Mix (x4). To meet the weekly dietary constraints, I would need to eat 79.4 servings of Tortilla Española and 25.84 servings of BOOST Drink Mix. The total of this diet is $109.24.
To meet the weekly dietary constraints and include at least one serving of each food, I would need to consume 1 serving of Kodiak Cakes Mix, 1 serving of Cheese, Fruit & Nut Packs, 78.15 servings of Tortilla Española, 25.16 servings of BOOST Drink Mix, and 1 serving of Madras Lentils. The total of this diet is $110.02, only $0.78 more than the original recommended diet.