A company manufactures and sells x digital cameras per week. The weekly price demand and cost are p=400-0.4x and c(x)=2000+160x
1. what price should the company charge for cameras, and how many cameras should be produced to maximize the weekly revenue? What is the maximum revenue?
2. What is the maximum profit? How much should the company charge for the cameras, and how many cameras should be produced to realize the maximum profit?


Thank you

First, the revenue that the company makes is equal to the camera's price per unit times the number of units sold, or Rev = x*p = x(400-.04x). You need to find determine this function's derivative and find the value for x where the derivative is zero. That will tell you how many cameras they should sell to either maximize or minimize revenue; to determine which it is, you can take the 2nd derivative. If the 2nd derivative at the point x is negative then you have a maximum; if it's positive then you have a minimum. Once you have the value of x for the maximum figured out, you can then plug that back into the equation for p to determine the selling price.

Profit is equal to revenue minus costs, or in this case x*p-(2000+160x). Again, you can find the value of x that maximizes profit by taking the derivative and setting it to zero.