A manufacturer of downhill and cross-country skis reports that manufacturing tim

Question

A manufacturer of downhill and cross-country skis reports that manufacturing time is 4 hours and 5 hours, respectively, per ski and that finishing time is 6 hours for each downhill and 2 hours for each cross-crountry ski. There are only 50 hours per week available for the manufacturing process and 42 hours for the finishing process. The average profit is $68 for downhill ski and $88 for cross-country ski. The manufacturer wants to know how many of each type of ski should be made to maximize the weekly profit.

Corner points of the feasible region:

Maximum profit is: $
when downhill skis
and cross country skis are produced.

Explanation / Answer

This is a simple maximization problem: you want to make the maximum amount of profit. For the sake of readability, x will represent the amount of downhill skis produced and y will represent the amount of cross-country skis produced. You want to maximize the equation: 72x + 89y Your constraints are the amount of hours: For manufacturing: x + 2y

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