A small manufacturing company makes and sells x machines each month. The monthly cost C, in dollars, of making x machines is given by C(x)= 2600+0.4x^2 The monthly income I, in dollars, obtained by selling x machines is given by I(x)=150x-0.6x^2 P(x) is the monthly profit obtained by selling x machines. a. Find P(x). b. Find the number of machines that should be made and sold each month to maximize P(x). c. Use yours answer to part b to find the selling price of each machine in order to maximize P(x).

Question

A small manufacturing company makes and sells x machines each month. The monthly cost C, in dollars, of making x machines is given by  C(x)= 2600+0.4x^2   The monthly income I, in dollars, obtained by selling x machines is given by  I(x)=150x-0.6x^2   P(x) is the monthly profit obtained by selling x machines.   a. Find P(x).  b. Find the number of machines that should be made and sold each month to maximize P(x).  c. Use yours answer to part b to find the selling price of each machine in order to maximize P(x).