Question

There are 3 factories on the Momiss River. Each emits 2 types of pollutants, labeled P1 and P2, into the river. If the waste from each factory is processed, the pollution in the river can be reduced. It costs $1500 to process a ton of factory 1 waste, and each ton processed reduces the amount of P1 by 0.10 ton and the amount of P2 by 0.45 ton. It costs $1000 to process a ton of factory 2 waste, and each ton processed reduces the amount of P1 by 0.20 ton and the amount of P2 by 0.25 ton. It costs $2000 to process a ton of factory 3 waste, and each ton processed reduces the amount of P1 by 0.40 ton and the amount of P2 by 0.30 ton. The state wants to reduce the amount of P1 in the river by at least 30 tons and the amount of P2 by at least 40 tons.

Required:
Formulate an LP that will minimize the cost of reducing pollution by the desired amounts. Do you think that the LP assumptions (Proportionality, Additivity, Divisibility, and Certainty) are reasonable for this problem?

Answer 1

Kindly check explanation

Step-by-step explanation:

Using table for our evaluation :

____________POLLUTANT

Factories___P1 ______P2 ____COST

__1_______0.1______ 0.45 ___ 1500

__2______ 0.2 _____ 0.25 ____1000

__3 ______0.40 ____ 0.30 ____2000

_________ ≥ 30 ____ ≥ 40 _____ z

Let amount of waste produced by Factories 1, 2 and 3 equal f1, f2 and f3 respectively.

Linear Program that will minimize the cost of reducing pollution by the desired amounts

Min cost:

min z = 1500f1 + 1000f2 + 2000f3

0.1f1 + 0.2f2 + 0.4f3 ≥ 30

0.45f1 + 0.25f2 + 0.3f3 ≥ 40

f1, f2, f3 ≥ 0