engineering economics

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 2,700 5,000 p = $38 + D 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 (c,) 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