Business Math Problem

Question

A pharmaceutical company must produce at least 132 liters of a drug by mixing two compounds. These compounds, the percentages of active ingredients and impurities in each, the amounts available and their costs are given below. The drug produced must contain at least 70% active ingredients and at most 0.6% impurities. If the company wishes to minimize its costs, how should the drug be mixed?

	A	B
Active ingredients	55%	75%
Impurities	0.2%	0.7%
Stock (in liters)	63	124
Cost (in dollars/liter)	$80	$90

Answer 1

this is a linear programming problem

with an objective function subject to constraints

graph the constraints, then check each vertex of the shaded area that satisfies all the constraints

pick the vertex which maximizes the objective function value

constraints

.55a +.75b =/> .7

.02a +.07b </= .06

63a +124b </= 132

a,b >/= 0

objective function

maximize 80a +90b