Question: A company produces and sells a consumer product, and is able to control the demand for the product by varying the selling price. The approximate price, p, and demand, D, is approximately
p = 38 + 2, 700/D for D ≥ 1
where p is the price per unit in dollars and D is the discrete demand per month. The company is seeking to maximize its net profit. The fixed cost is S1000 per month and variable cost is proportional to $D.
a. What is the optimal number of units that should be produced and sold each month?
b. Show that your answer in part (a) maximizes profits.
c. What is the unit price of your answer in part (a)?