Project ForgePlant Design & Economics
Profitability Analysis
GATE 2013
Hard
A plant manufactures compressors at the rate of N units/day. The daily fixed charges are Rs. 20000 and the variable cost per compressor is Rs. 500+0.2N^1.3. The selling price per compressor is Rs. 1000. The number of compressors to be manufactured, to the nearest integer, in order to maximize the daily profit is _____
217 units/day(± 1.5 accepted)
Explanation
Profit=1000N−20000−N(500+0.2N^1.3)=500N−20000−0.2N^2.3. d(Profit)/dN=500−0.46N^1.3=0 ⟹ N^1.3=1086.96 ⟹ N=1086.96^(1/1.3)≈216.6, rounding to the profit-maximizing integer N≈217 (checked: profit at N=217 exceeds that at N=216 or N=218).
Source: GATE CH 2013 (2013)
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