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 manuacturing data are given in the table. Trick Ski - 8 hours of fabricating and 1 hour for finishing Slalom Ski - 6 hours of fabricating and 1 hour for finishing Maximum Labor Hours avail per Day are 312 for Fabricating and 48 for Finishing. If the profit on a trick ski is $60 and the profit on a slalom ski is $40, how many of each type of ski should be manufactured each day to realize a maximum profit? What is the maximum profit? Answer as The maximum profit is $_____. The maximum occurs when ___trick skis and ____slalom skis are produced.

Explanation / Answer

I made this spreadsheet by fixing the value for trick skis in the first column.

In the second column I choose the minimum of:

48 - t (the number of slalom skis that could be finished in remaining time)

and

(312 - 8t)/ 6 (this is the number of slalom skis that could be fabricated in remaining time; Rounded down to the nearest integer)

Then I used P = 60t + 40s to calculate profit in the 3rd column.

The maximum profit is $2320 making 36 trick skis and 4 slalom skis.

Trick Skis Slalom Skis Profit 0 48 1920 1 47 1940 2 46 1960 3 45 1980 4 44 2000 5 43 2020 6 42 2040 7 41 2060 8 40 2080 9 39 2100 10 38 2120 11 37 2140 12 36 2160 13 34 2140 14 33 2160 15 32 2180 16 30 2160 17 29 2180 18 28 2200 19 26 2180 20 25 2200 21 24 2220 22 22 2200 23 21 2220 24 20 2240 25 18 2220 26 17 2240 27 16 2260 28 14 2240 29 13 2260 30 12 2280 31 10 2260 32 9 2280 33 8 2300 34 6 2280 35 5 2300 36 4 2320 37 2 2300 38 1 2320 39 0 2340 40 -2 2320 41 -3 2340 42 -4 2360 43 -6 2340 44 -7 2360 45 -8 2380 46 -10 2360 47 -11 2380 48 -12 2400

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