Chapter 3.4, Problem 1P

Explanation of Solution

Given:

From the given scenario, it is given that the three factories are available on the Momiss River. There are two types of pollutants emitted into the river and the if the waster form the factory is processed, the pollution in the river can be reduced.

Processing cost for factory 1 waste: $15

Processing cost for factory 2 waste: $10

Processing cost for factory 3 waste: $20

Consider the variable to represent the amount of waste in factory 1 is $x_1$

Consider the variable to represent the amount of waste in factory 2 is $x_2$

Consider the variable to represent the amount of waste in factory 3 is $x_3$

$\begin{array}{l}\text{Total cost}=\left\{\begin{array}{l}\text{(Dollars per ton of factory 1 waste)(Amount of waste in factory1)+}\\ \text{(Dollars per ton of factory 2 waste)(Amount of waste in factory2)+}\\ \text{(Dollars per ton of factory 3 waste)(Amount of waste in factory3)}\end{array}\right\}\\ =15x_1+10x_2+20x_3\\ \end{array}$

The objective function obtained from the above calculation is

$\text{Maximize}z=15x_1+10x_2+20x_3$

Considering the constraints,

Constraint 1: At least 30 tons of pollutant 1 must be reduced in the river.

Constraint 2: At least 40 tons of pollutant 2 must be reduced in the river