Chapter 3.2, Problem 5P

Explanation of Solution

Determining the number of acres of corn and wheat to plant:

Let $x_1$ be the number of desks produced and $x_2$ be the number of chairs produced.

Objective function:

$\text{Maximize}{\text{z = 40x}}_{\text{1}}{\text{+25x}}_{\text{2}}$

Considering the constraints,

Constraint 1: Maximum 20 units of wood are available.

Constraint 2: Sell twice as many as chairs as desks.

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

$4x_1+3x_2\le 20$

Expressing the constraint 2 in terms of $x_1$ and $x_2$:

$x_1\ge 2x_2$

Mathematical model of given LP is,

$\text{Maximize}{\text{z = 40x}}_{\text{1}}{\text{+25x}}_{\text{2}}$