Chapter 3.4, Problem 3P

Explanation of Solution

a.

Given:

Let $x_1$ and  $x_2$ be the pounds of food 1 and food 2 purchased.

The objective function is

$\text{Maximize}z=7x_1+x_2$

Considering the constraints,

Constraint 1: At least 12 units of vitamin A is required.

Constraint 2: At least 6 units of vitamin C is required.

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

$3x_1+x_2\ge 12$

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

$x_1+x_2\ge 6$

Mathematical model of given LP is,

$\text{Maximize}z=7x_1+x_2$

Subject to the constraints,

$\begin{array}{l}3x_1+x_2\ge 12(\text{Vitamin A}\text{constraint)}\\ x_1+x_2\ge \end{array}$

Explanation of Solution

b.

$\text{Maximize}z=7x_1+x_2$

Subject to the constraints,

$\begin{array}{l}3x_1+x_2\ge 12(\text{Vitamin A}\text{constraint)}\\ x_1+x_2\ge 6\text{(Vitamin C}\text{constraint)}\end{array}$