Problem:

The Hickory Cabinet and Furniture Company has decided to concentrate on the production of chairs. The fixed cost per month of making chairs is $7,500, and the variable cost per chair is $40. Price is related to demand according to the following linear equation:

v = 400 - 1:2p;

where v is the demand and p is the price.

Required:

Question 1) Develop the nonlinear profit function for this company and determine the price that will maximize profit, the optimal volume, and the maximum profit per month.

Provide correct solution for the problem and show all work.