The fixed monthly cost to operate a plywood factory is $1 million and the variable cost is $131.50 per 1000 board feet of product. The company estimates that the plywood will sell for p = $700 - (0.05)D, where D is measured in units of 1000 board feet.
a) Determine the optimum monthly sales volume for the plywood factory, and calculate the profit (or loss) at the optimal volume.
b) Determine the range of profitable monthly demand for plywood.
c) On a single graph, plot the profit as a function of demand (for 0<=D<=12,000) and the selling price as a function of demand.

A company estimates that the relationship between the unit price and the monthly demand for a new product is p = $100 - (0.10)D. The fixed costs for producing the product are $17,500 per month and the estimated variable cost of production is $40 per unit.
a) What is the optimal demand, D*, and based on this demand, should the company produce the product? Why?
b) Plot the profit as a function of demand for 0<=D<=1000.

A plant has a capacity of 4,100 units per month. When it operates, the plant has a fixed cost of a $504,000 per month. The product sells for $328 per unit and has a variable cost of $166 per unit.
a) What is the breakeven point in the number of units per month?
b) What are the corresponding percentage reductions in the breakeven point if the fixed costs decrease by 9%, 18%, and 27%?
c) What are the percentage reductions in the breakeven point if the variable costs decrease by 3%, 6%, and 9%?