A manufacturer of skis produces two types: downhill and cross country. The times required for manufacturing and finishing each ski are: manufacturing time per ski, downhill 2.5 hours, cross country 1.5 hours. Finishing time per ski: downhill 0.5 hours, cross country 1.5 hours. The maximum total weekly hours available for manufacturing and finishing the skis are 90 hours and 42 hours. The profit per ski are $50 for downhill and $50 cross country. Determine how many of each kind of ski should be produced to achieve a maximum profit?

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AlonsoDehner AlonsoDehner · Answer 1 · 2020-02-04T09:05:57+01:00

Answer:

So to maximize profit 24 downhill and 20 cross country shouldbe produced

Step-by-step explanation:

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

Time required for manufacturing and finishing each ski are: manufacturing time per ski, downhill 2.5 hours, cross country 1.5 hours

Finishing time per ski: downhill 0.5 hours, cross country 1.5 hours.

Total manufacturing time taken = (2.5) x+ (1.5+) y = 2.5x+1.5y≤90

total finishing time taken = 0.5x+1.5 y≤42

Profit function

Z = 50x+50y

Objective is to maximize Z

Solving the two equations we get intersecting point is

(x,y) = (24,20)

In the feasible region corner points are (0.28) (36,0)

Profit for these points are

i) 2200 for (24,20)

ii) 1400 for (0,28)

iii) 1800 for (36,0)

So to maximize profit 24 downhill and 20 cross country shouldbe produced.