A firm is planning to manufacture a new product. As the selling price is increased, the quantity that can be sold decreases. Numerically they estimate
P = $35.00 - 0.02Q
(P = selling price per unit, Q = quantity sold per year)
On the other hand, management estimates that the average cost of manufacturing and selling the product will decrease as the quantity sold increases
C = $4.00Q + $8000
where C = cost to produce and sell Q per year
The want to maximize profit. What quantity should the decision makers plan to produce and sell each year?