Question

MCS Chemicals uses chemicals (1 and 2) to manufacture two products (A and B). Product A must be at least 60% chemical 1, and Product B must be at least 40% chemical 2. Up to 60 oz of Product A can be sold at $10 per oz; up to $25 oz of Product B can be sold at $8 per oz. Up to 50 oz of Chemical 1 can be purchased at $6 per oz, and up to 40 oz of Chemical 2 can be purchased at $4 per oz.

1- Formulate the model

2- Solve the LP model of part 1 to maximize the company's profits.

Answer 1

1) LP model is following:

Let A1 and A2 be the quantity (oz) of chemical 1 and 2 used in production of product A

and B1 and B2 be the quantity (oz) of chemical 1 and 2 used in production of product B

Maximize 10A1 + 10A2 + 8B1 + 8B2 - 6A1 - 6B1 - 4A2 - 4B2

s.t.

A1 >= 0.6*(A1+A2)

B2 >= 0.4*(B1+B2)

A1+A2 <= 60

B1+B2 <= 25

A1+B1 <= 50

A2+B2 <= 40

A1, A2, B1, B2 >= 0

2) Solution of LP model using Solver is following:

EXCEL FORMULAS:

Optimal production schedule:

Product A to be produced = 36+24 = 60 oz

Product B to be produced = 9+16 = 25 oz

Chemical 1 to be purchased = 36+9 = 45 oz

Chemical 2 to be purchased = 24+16 = 40 oz

Total profit = $ 370