Exercise $4(20$ points$)$

A large wood products company is negotiating a contract to sell plywood overseas. The fixed cost of the company which can be allocated to the production of the plywood is $$1,000,000$ per month. The variable cost per thousand board feet is $$131\mathrm{.}50.$ Price charged will be determined by $p=$$$700-(0\mathrm{.}05)D$ per $1000$ board feet.

a$.$ For this situation, determine the optimal monthly sales volume for this product and calculate the profit $($or loss$)$ at the optimal volume. $(10$ points$)$

b$.$ What is the range of profitable demand during a month? $(10$ points$)$