Chapter 3.4, Problem 2P

Explanation of Solution

Given:

Let $x_1$ , $x_2$ and $x_3$ are the cost of pig value purchased from supplier 1, supplier 2 and supplier 3.

The total cost of the pig valve can be obtained from the cost of each value for each supplier when the number of valves are $x_1$ , $x_2$ and $x_3$.

The objective function can be

$\text{Maximize}z=5x_1+4x_2+3x_3$

Considering the constraints,

Constraint 1: At least 500 large valves must be purchased with each supplier.

Constraint 2: At least 300 medium valves must be purchased with each supplier.

Constraint 3: At least 300 small valves must be purchased with each supplier.

Constraint 4: At least 700 small valves must be purchased from each supplier.

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

$40x_1+30x_2+20x_3\ge 500$

Expressing the constraint 2 in terms of $x_1$, $x_2$and $x_3$ :

$40x_1+35x_2+20x_3\ge 300$

Expressing the constraint 3 in terms of ${}_{}$