| course |
course_year |
question_number |
tags |
title |
year |
Optimization |
IB |
66 |
|
Paper 4, Section II, H |
2011 |
A company must ship coal from four mines, labelled $A, B, C, D$, to supply three factories, labelled $a, b, c$. The per unit transport cost, the outputs of the mines, and the requirements of the factories are given below.
\begin{tabular}{c|c|c|c|c|c}
& $A$ & $B$ & $C$ & $D$ & \
\hline$a$ & 12 & 3 & 5 & 2 & 34 \
\hline$b$ & 4 & 11 & 2 & 6 & 21 \
\hline$c$ & 3 & 9 & 7 & 4 & 23 \
\hline & 20 & 32 & 15 & 11 &
\end{tabular}
For instance, mine $B$ can produce 32 units of coal, factory a requires 34 units of coal, and it costs 3 units of money to ship one unit of coal from $B$ to $a$. What is the minimal cost of transporting coal from the mines to the factories?
Now suppose increased efficiency allows factory $b$ to reduce its requirement to $20.8$ units of coal, and as a consequence, mine $B$ reduces its output to $31.8$ units. By how much does the transport cost decrease?