A factory manufactures two kinds of ice skates: racing skates and figure skates. The racing skate requires 8 work-hours in the fabrication department, whereas the figure skate requires 7 work-hours in the fabrication department. The racing skate requires 1 work-hour in the finishing department, whereas the figure skate requires 3 work-hours there. The fabricating department has available at most 208 work-hours per day, and the finishing department has no more 60 work-hours per day available. If the profit on each racing skate is $8 and the profit on each figure skate is $10, how many of each should be manufactured each day to maximize profit? (Assume that all skates made are sold.)

## Pre calculus

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# 1 Answer

**Problem**: To maximize

8R + 10F [profit]

subject to the two constraints

8R + 7F <= 208 [fab dept],

R + 3F <= 60 [fin dept].

Work with this and if you would like more help, I or another tutor will be happy to assist you.

## Comments

Robert has just given you the solution,

Solve two simultaneous equations without the inequality sign

8R+7F = 208

R+3F = 60

you will get the values of R and F on solving both of them, which makes sense as given the constrains all the time available must be utilized in production of the skates.

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