A firm is planning to manufacture a new product. The sales department estimates that the quantity that can be sold depends on the selling price. As the selling price is increased, the quantity that can be sold decreases. Numerically they estimate:
On the other hand, management estimates that the average cost of manufacturing and selling the product will decrease as the quantity sold increases. They estimate
C = $4.00Q + $8000
where C = cost to produce and sell Q per year
The firm's management wishes to produce and sell the product at the rate that will maximize profit, that is, income minus cost will be a maximum. What quantity should the decision makers plan to produce and sell each year?