Chapter 3.1, Problem 1P

Explanation of Solution

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

Let $x_1$ be the number of acres of corn planted and $x_2$ be the number of acres of wheat planted.

Weekly revenue is calculated as follows:

$\begin{array}{l}\text{Weekly revenues=weekly revenue from corn+weekly revune from wheat}\\ =\left\{\begin{array}{l}\text{(dollars/corn)(corn bushels/acre)}\\ \text{+(dollars/wheat bushel)(wheat bushels/acre)}\end{array}\right\}\\ =(3\times 10)x_1+(4\times 25)x_2\\ =30x_1+100x_2\\ \end{array}$

The object function obtained from the above calculation is

$\text{Maximize}{\text{z = 30x}}_{\text{1}}{\text{+100x}}_{\text{2}}$

Considering the constraints,

Constraint 1: Seven acres of land is available.

Constraint 2: 40 hours of labor are available each week.

Constraint 3: At least 30 bushels of corn must be produced