Asked by Anshul Kansal | 26th Apr, 2013, 12:13: PM

Expert Answer:

Let the company produce x deluxe model and y ordinary model article
Hence, the total time spent by 5 skilled men = 2x+y and it should be less than 8hours/person
Hence, 2x+y <=40 (1)
Also, the total time spent by 10 semi-skilled men = 2x+3y and it should be less than 8hours/person
Hence, 2x+3y <=80 (2)
Also, x>=0 (3) and y>=0 (4)
Profit = 15x+10y
We need to maximise profit given the constraints. So, for that draw all the 4 lines on the graph and check the common area, you will form a hexagon OABC with A(0,80/3); B(10,20); C(20,0); O(0,0)
Since the feasible region is a bound region, we can check the profit function at all the vertices to find the point of maxima
At point A: 15(0)+10(80/3) = 800/3
At point B: 15(10)+10(20) = 350
At point C: 15(20)+10(0) = 300
At point 0: 15(0)+10(0) = 0
So, the maxima lies at point C with x =10and y = 20 and the maximum profit = Rs 350.

Answered by  | 27th Apr, 2013, 09:37: AM

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