Section 11.8

Linear Programming

OBJECTIVE 1

OBJECTIVE 2

Consider the linear programming problem

Maximize: 0.05 0.08

subject to the conditions that

0

0

30

20

5

I x y

x

y

x y

x

y

Minimize the expression 3 4

subject to the constraints

7 10 5 0 0

z x y

y x x y x y

A factory manufactures two kinds of ice skates: racing skates and figure skates. The racing skates require 8 work hours in the fabrication department, whereas the figure skates require 4 work hours there. The racing skates and the figures skates each require 2 work hours in the finishing department. The fabricating department has available at most 224 work hours per day, and the finishing department has no more than 72 work hours per day available. If the profit on each racing skate is $15 and the profit on each figure skate is $12, how many of each should be manufactured each day to maximize profit? (Assume that all skates made are sold.)