the cost of producing x units of product is denoted by 99,000/x +100 x +50000
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Profit will be Pro(x)=xP−C(x)
Pro(x)=x(200−
400
x
)−(
100
x
2
+100x+40)
We want to maximize Pro(x) so differentiate it w.r.t x and put it =0
dx
d(Pro(x))
=200−
400
2x
−
100
2x
−100=0→x=4000
Hence, price per unit will be P=200−
400
4000
=190
Total Profit will be Pro(x)=4000×190−(
100
(4000)
2
+100×4000+40)=32×10
4
−40=319960.
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