A firm is planning to manufacture a new product. The sale department estimates t

Question

A firm is planning to manufacture a new product. The sale department estimates that the quantity that can be sold depends on the selling price. As the seller price is increased, the quantity that can be sold decreases. Numerically they estimate P-$35.00-0.020 Where P- selling price per unit Qe quantity sold per year On the other hand, the management estimates that the average cost of manufacturing and selling the product will decrease as the quantity sold increases. They estimate C $4.000+$8000 Where C-cost to produce and sell the product at the rate that will maximize profit, that is where income minus cost will be a maximum. What quantity should the decision makers plan to produce and sell each year DOLL F10 F11 F12 PrtScr F9 F7 F5 Pu 8 9 5 6

Explanation / Answer

Profit = Revenue - cost

= PQ - C

= (35 - 0.02Q)Q - (4Q + 8000)

= 35Q - 0.02Q^2 - 4Q - 8000

= 31Q - 0.02Q^2 - 8000

Profit is maximized when the derivative of profit function is set = 0

31 - 0.04Q = 0

Q = 775 units

Hence profit maximizing quantity is 775 units.

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