Chapter 3, Problem 17RP

Explanation of Solution

Given:

Let $x_1$  be the number of tables produced by oak and $x_2$ be the number of chairs produced by oak.

Let $y_1$  be the number of tables produced by pine and $y_2$ be the number of chairs produced by pine.

Objective function:

$\text{Revenues=}\left(\frac{\text{cost}}{\text{table}}\right)\text{(number of tables produced)+}\left(\frac{\text{cost}}{\text{chair}}\right)\text{(number of tables produced)}$

$\text{Maximize}z=40(x_1+y_1)+15(x_2+y_2)$

Considering the constraints,

Constraint 1: At least 150 board ft of oak is available

Constraint 2: : At least 210 board ft of oak is available

Expressing the constraint 1 in terms of $x_1$, $x_2$and $x_3$ :

$\left[\begin{array}{l}\text{(17 board ft of oak/table)(number of tables produced from oak)}\\ \text{+(5 board ft of oak/chair)(number of chairs produced from oak)}\end{array}\right]\&$