A company has established that the relationship between the sales pnce for one o

Question

A company has established that the relationship between the sales pnce for one of its products and the quantity sold per monthis approximate = 70-0.30 O is the demand or quantity sold per month and p is the price in dollars). The fixed cost is $600 per month and the variable cost is $30 per unit produced. a. What is the maximum profit per month for this produek? b. What is the range of profitable demand during a month? a. The maximum proft per month for this product is (Round to the nearest dolar.)

Explanation / Answer

Demand is given by P = 70 - 0.3Q. Then revenue becomes R = 70Q - 0.3Q^2. Cost is C = 600 + 30Q

Profit = R - C

= 70Q - 0.3Q^2 - (600 + 30Q)

= 40Q - 0.3Q^2 - 600

a) Profit is maximum when marginal profit is 0. 40 - 0.6Q = 0 or Q = 40/0.6 = 66.67 and price P = 70 - 0.3*66.67 = $50 per unit. Profit = 40*66.67 - 0.3*(66.67^2) - 600 = $733

b) Range of profitable demand is given by the roots of 40Q - 0.3Q^2 - 600 which are 17 and 116. Hence the relevent range is 18 units and 116 units.

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