Question

If the demand function of a firm a P = (80-x)^2and average cost function ( is Ac=55-8x A find the output level at which the profit level is maximum
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Answer 1

Answer:

The profit function is given by

P(x)=xp(x)−C(x)

=x(10−0.001x)−(50+5x)

=10x−0.001x

2

−50−5x

=5x−0.001x

2

−50

Take the derivative of P(x) :

P

′

(x)=5−0.002x

So, the critical point is

x=2500

Since, the second derivative of P(x) is negative, x=2500 is a point of maximum.

Hence, the company has the largest profit when x=2500.