To maximize profit 14 downhill and 24 cross country should be produced.
<h3>How to find the intersecting point?</h3>
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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( here 2y is GCF common term so taking outside the terms of the polynomial )
( now taking (-) outside )