Handy Vac manufactures and distributes a line of feather dusters. Demand per period (Q) for the Vac-O-Matic, their most popular feather duster, has the relationship:
Q = 500 - (1/2)P
Where P is price. Total costs (with a "normal" distribution to the unit holders included) of producing Q units per period are:
TC = 10,000 + 50Q + 3Q2
(a) Determine the total revenue (TR) and total profits in terms of Q.
(b) At what level of output (Q) are total profits maximized? What price will be charged? What are total profits at this output level?
The problem set deals with estimating the total cost, average cost and point where profit is maximized from provided information.