Chapter 5.1, Problem 1P

Explanation of Solution

Optimal solution

• The number of soldiers produced each week is $\text{x}$ and the number of trains produced each week is $\text{y}$.
• Weekly revenues and costs can be expressed in terms of x and y.

  $\text{Weekly revenues = 27x + 21y}\text{.}$

  $\text{Weekly raw material costs = 10x + 9y}\text{.}$

  $\text{Other weekly variable costs = 14x + 10y}\text{.}$

  • Hence $\text{profit = 27x + 21y – }\left(\text{10x + 9y}\right)\text{ – 14x + 10y = 3x + 2y}$
  • The constraints are

    $\begin{array}{l}\text{2x + y <= 100}\hfill \end{array}$