Question

The demand function of a monopolist is
p=12 - 4x and the cost function is C =8x – x^2
The maximum profit is:​

Answer 1

Answer:

x = 2500

Step-by-step explanation:

The profit function is given by 

P(x)=xp(x)−C(x)

=x(10−0.001x)−(50+5x)

=10x−0.001x2−50−5x

=5x−0.001x2−50

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.