Question

A chemical manufacturer uses chemicals 1 and 2 to produce two drugs. Drug 1 must be at least 25% chemical 1, and drug 2 must be at least 60% chemical 2. Up to 50,000 ounces of drug 1 can be sold at $27 per ounce; up to 60,000 ounces of drug 2 can be sold at $26 per ounce. Up to 45,000 ounces of chemical 1 can be purchased at $19 per ounce, and up to 55,000 ounces of chemical 2 can be purchased at $18 per ounce. Use solver to determine how to maximize the manufacturer’s profit. How much of chemical 2 should be used to produce drug 2?

Answer 1

Let ounces be the quantity of chemicals i required to produce the drug j, where i=1,2 and j=1,2

These are the decision variables.

The total quantity of drug 1 produced is

ounces

The total quantity of drug 2 produced is

drug 1 can be sold at $27 per ounce; and drug 2 can be sold at $26 per ounce.

The total revenue form selling of drug 1 and of drug 2 is

chemical 1 can be purchased at $19 per ounce, and chemical 2 can be purchased at $18 per ounce

The total cost of the chemicals used is

The net profit is

We want to maximize this profit, and hence this is the objective function

Next, the constraints

Drug 1 must be at least 25% chemical 1

drug 2 must be at least 60% chemical 2

Up to 50,000 ounces of drug 1 can be sold

up to 60,000 ounces of drug 2 can be sold

Up to 45,000 ounces of chemical 1 can be purchased

up to 55,000 ounces of chemical 2 can be purchased

The LP model is

Maximize

s.t.

Prepare the following

get this

set the solver using data--->solver

get this

To maximize the profit, we should produce

• 50,000 ounces of drug 1 using 45,000 ounces of chemical 1 and 4500 ounces of chemical 2.
• 50,000 ounces of drug 2 using 0 ounces of chemical 1 and 50,000 ounces of chemical 2.

ans: 50,000 ounces of chemical 2 should be used to produce drug 2