Find the production level that will maximaze the profit P(x)=R(x)-C(x)

Question

For the given cost function

C(x)=3000+640x+1.1x² and the demand function p(x)=1920. the price p at the given volume of demand x) .
Find the production level that will maximaze the profit P(x)=R(x)-C(x), where R(x) is the revenue function. 

Answer 1

Profit is maximized when the Cost is minimized, since demand , the revenue is fixed

 

C(x) = 1.1X^2 - 640X + 3000

 

The coefficient of X has to be -640, otherwise it will give negative value for production unit.

 

  Vertex = 640/ 2(1.1) = 290.9 ≈291 units