A large wood products company is negotiating a contract to sell plywood overseas. The fixed cost that can be allocated to the production of plywood is $800,000 per month. The variable cost per thousand board feet is $155.50. The price charged will be determined by p = $600 - (0.5)D per 1,000 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.
b. What is the domain of profitable demand during a month?