A large company in the communication and publishing industry has quantified the

Question

A large company in the communication and publishing industry has quantified the relationship between the price of one of its products and the demand for this product as Price-140-0.02 x Demand for an annual printing of this particular product. The fixed costs per year (i.e., per printing) $54,000 and the variable cost per unit-S40. What is the maximum profit that can be achieved? What is the unit price at this point of optimal demand? Demand is not expected to be more than 3,000 units per year The maximum profit that can be achieved is s(Round to the nearest dollar.) The unit price at the point of optimal demand is per unit. (Round to the nearest cent.)

Explanation / Answer

The demand function is P = 140 - 0.02Q. FC = 54000 and VC = 40Q.

Profit = Revenue - Cost = PQ - FC - VC  

= (140 - 0.02Q)Q - 54000 - 40Q where Q < or = 3000

= 100Q - 0.02Q^2 - 54000

Profit is maximum when derivative of profit = 0

100 - 0.04Q = 0

Q = 2500.

Price = 140 - 0.02*2500 = $90.

Maximum profit = 2500*90 - 54000 - 40*2500 = $71,000

The price is $90 per unit

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