A manufacturing company makes two types of water skis, a trick ski and a slalom

Question

A manufacturing company makes two types of water skis, a trick ski and a slalom ski. The relevant manufacturing data are given in the table. Labor-Hours per Ski Maximum Labor-Hours Available per Day 168 30 Trick Sk Department Fabricating Finishing Slalom Ski If the profit on a trick ski is $40 and the profit on a slalom ski is $30, how many of each type of ski should be manufactured each day to realize a maximum profit? What is the maximum profit? The maximum profit is The maximum occurs when trick skis and slalom skis are produced.

Explanation / Answer

Let,

Quantity of Trick Ski = T

Quantity of Stalom Ski = S

Profit = 40*T + 30*S

Subject to constraints:

6T + 4S 168

T + S 30

T 0

S 0

Equating the constraints,

6T + 4S = 168 ------------------ (1)

4T + 4S = 120 ------------------ (2)

Subtracting eq. 2 from 1,

2T = 48

T = 24

S = (120-96)/4

S = 6

Hence,

Maximize profit = 40*24 + 30*6

Maximize profit = $1140

Quantity of Trick Ski = 24

Quantity of Stalom Ski = 6

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