Chapter 6, Problem 30RE

In problems 38-41, construct a mathematical model in the form of a linear programming problem (The answer in the back of the book for these application problems include the model.) Then solve the problem by the simplex, dual problem, or big $M$ methods.

Shipping schedules. A company produces motors for washing machines at factory $A$ and factory $B$. The motors are then shipped to either plant $X$ or plant $Y$, where the washing machines are assembled. The maximum number of motors that can be produced at each factory monthly, the minimum number required for each plant to meet anticipated demand, and the shipping charges for one motor are given in the table. Determine a shipping schedule that will minimize the cost of transporting the motors from the factories to the assembly plants.

$\begin{array}{cccc}& \text{Plant }X& \text{Plant }Y& \begin{array}{l}\text{Maximum}\\ \text{Production}\end{array}\\ \text{Factory }A& \text{\$}5& \text{\$}8& 1,500\\ \text{Factory }B& \text{\$}9& \text{\$}7& 1,000\\ \text{Minimum Requirement}& 900& 1,200& \end{array}$