A chemical manufacturer uses chemicals 1 and 2 to produce two drugs. Drug 1 must

Question

A chemical manufacturer uses chemicals 1 and 2 to produce two drugs. Drug 1 must be at least 70% chemical 1 and drug 2 must be at least 60% chemical 2. Up to 50,000 ounces of drug 1 can be sold at $30 per ounce; up to 60,000 ounces of drug 2 can be sold at $25 per ounce. Up to 45,000 ounces of chemical 1 can be purchased at $15 per ounces, and up to 55,000 ounces of chemical 2 can be purchased at $18 per ounce. Formulate this problem as a linear programming model to determine how to maximize the manufacturer's profit. You only need to formulate this problem. No need to solve it.) ParagraphB I

Explanation / Answer

Characterize factors:

A = ounces of medication A to be created

B = ounces of medication B to be created

C1 = ounces of concoction 1 acquired (and utilized)

C2 = ounces of concoction 2 acquired (and utilized)

X1A = ounces of concoction 1 used to deliver sedate A

X2A = ounces of synthetic 2 used to create tranquilize A

X1B = ounces of substance 1 used to deliver medicate B

X2B = ounces of compound 2 used to deliver medicate B

- - -

Objective:

Augment 30A + 25B - 15C1 - 18C2

- - -

Medication An is made completely out of synthetic compounds 1 and 2: A = X1A + X2A

Medication B is made totally out of synthetic compounds 1 and 2: B = X1B + X2B

Utilization of compound 1 is constrained by the sum bought: X1A + X1B < = C1

Utilization of compound 2 is constrained by the sum bought: X2A + X2B < = C2

Synthetic 1 must be no less than 70% of medication A: X1A > = 0.7A

Compound 2 must be no less than 60% of medication B: X2B > = 0.6B

A most extreme of 50000 ounces of medication A can be delivered: A <=50000

A most extreme of 60000 ounces of medication B can be delivered: B <=60000

A most extreme of 45000 ounces of synthetic 1 can be bought: C1 <= 45000

A most extreme of 55000 ounces of synthetic 2 can be bought: C2 <= 55000

All factors are limited to be nonnegative

MAX:30A + 25B - 15C1 - 18C2

SUBJECT TO

A - X1A - X2A = 0

B - X1B - X2B = 0

- C1 + X1A + X1B <= 0

- C2 + X2A + X2B <= 0

- 0.7 A + X1A >= 0

- 0.6 B + X2B >= 0

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