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 relationship between price and demand is
p = $38 +2,700/D −5,000/D2, for D > 1,
where p is the price per unit in dollars and D is the demand per month.
The company is seeking to maximize its profit. The fixed cost is $1,000 per month and the variable cost (Cv) is $40 per unit.
a. What is the number of units that should be produced and sold each month to maximize profit?
b. Show that your answer to Part (a) maximizes profit