Question

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

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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