Defining total profits as the difference between total

Question

Defining Q to be the level of output produced and sold, the cost function for is given by the relationship

 

            TC = 5 - 30Q                         

 

Additionally, the demand function facing the firm is

 

            Q = 11.5 - 0.05P, where P is the price per unit of the good.

 

1. Defining total profits as the difference between total revenue and total cost, express in terms of Q the total profit function of the firm.

 

1. Determine the output level where total profits are maximized.  Show that profit is maximized, rather than minimized.

 

1. Calculate total profits and selling price at the profit-maximizing output level.

 

1. Show that profit maximization occurs where MR = MC.