1. 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 (c) is $40 per unit. a. What is the number of units that should be produced and sold each month to maximize total revenue? b. What is the number of units that should be produced and sold each month to maximize profit? c. What is the profitable range of the demand?

1. 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 (c) is $40 per unit. a. What is the number of units that should be produced and sold each month to maximize total revenue? b. What is the number of units that should be produced and sold each month to maximize profit? c. What is the profitable range of the demand?