Question

A manufacturer of skis produces 2 types: downhill and cross country. Times for manufacturing each ski are given

Manufacturing each ski: Downhill 3 hours Cross Country 2.5 hrs

Finishing time per ski: Downhill 0.5 hours Cross Country 0.5 hours

The maximum total weekly hours available for manufacturing and finishing the skis are 102 hrs. and 19 hrs respectively. The profits per ski are $80 downhill and $90 cross country. Determine how many of each kind of ski should be produced to achieve a maximum profit.

Answer 1

To maximize profit 14 downhill and 24 cross country should be produced.

How to find the intersecting point?

Let X represent the number of downhill skis and Y represent the number of cross country skis.

Manufacturing each ski: Downhill 3 hours Cross Country 2.5 hrs

Finishing time per ski: Downhill 0.5 hours Cross Country 0.5 hours

Total manufacturing time taken = (3)x+ (2.5+) y = 3x +2.5y ≤ 102

total finishing time taken = 0.5x+0.5 y ≤ 19

Profit function

Z = 80x + 90y

The objective is to maximize Z

By solving the two equations we get an intersecting point

(x,y) = (14,24)

In the feasible region corner points are (0, 36) (41,0)

So to maximize profit 14 downhill and 24 cross country should be produced.

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