Chapter 4.17, Problem 1P

Explanation of Solution

Solution:

Let,

${\text{x}}_1$= Number of valves purchased from supplier 1

${\text{x}}_{\text{2}}$= Number of valves purchased from supplier 2

${\text{x}}_3$= Number of valves purchased from supplier 3

$z$= Cost of purchasing valves

The size mix and cost of the valves given in the tale below,

Supplier	Cost Per value (S)	Percent Large	Percent Medium	Percent Small
1	5	40	40	20
2	4	30	35	35
3	3	20	20	60

Then, the total cost of the valves can be expressed as,

$z={\text{5x}}_1{\text{+4x}}_{\text{2}}+3{\text{x}}_3$

In each month, at least 500 large valves should be purchased. Therefore, the constraint can be written as,

$\text{0}{\text{.4x}}_{\text{1}}\text{+0}{\text{.3x}}_{\text{2}}\text{+0}{\text{.2x}}_{\text{3}}\ge \text{500}$

In each month, at least 300 medium valves should be purchased. Therefore, the constraint can be written as,

$\text{0}{\text{.4x}}_{\text{1}}\text{+0}{\text{.35x}}_{\text{2}}\text{+0}{\text{.2x}}_{\text{3}}\ge 3\text{00}$

In each month, at least 300 small valves should be purchased. Therefore, the constraint can be written as,

$\text{0}{}_{}$