Suppose that the weekly profit for an electronics store gene

Suppose that the weekly profit for an electronics store generated from the sale of x iPods is given by the function P(x) = - 3x2 +270x - 4200 where P(x) is in dollars. What is the maximum weekly profit from the iPod sales?

Solution

Answer:

The profit function P(x) is given by

P(x) = - 3x² +270x - 4200

To find the maximum of P(x) we set the derivative of P(x) with respect to x to zero.

That is P\'(x) = - 6x +270 = 0

                    6x = 270

                   x = 270 / 6

               x = 45

Therefore the maximum of profit is P(45) = - 3(45)² +270(45) - 4200

                                                      P(45) = 1875

Hence , the maximum of profit is $ 1875