Can anyone help me slove this question?

Question

A company finds that if they price their product at $ 35, they can sell 235 items of it. For every dollar increase in the price, the number of items sold will decrease by 5. What is the maximum revenue possible in this situation? and What price will guarantee the maximum revenue?

Answer 1

Let x = the number of $1 decreases in price.  The number of items produced will be 235 + 5x.  The price will be $35 - x.  The revenue, R(x), will be:

 

R(x) = (235 + 5x)($35-x) = 5875 - 60x - 5x²

 

To optimize, take the derivative of R(x) wrt x, set it to zero, and solve for x. That will give you the number of $1 decreases in price that will optimize revenue. Plug that value of x into the Revenue equation above to find the maximum revenue. The optimal price will be $35-x.