Normally the selling price of a product, p, is related to the demand according t

Question

Normally the selling price of a product, p, is related to the demand according to the following relationship: p = a – bD.
However, a company has found that the price (in dollars) of its product can be related to demand, D, according the following different equation:

p = 88.5 – 0.08(D0.75)

Demand is given in units per year. In addition, there is a fixed cost of $40,000 per year and a variable cost to manufacture the product is $40 per unit.

Determine the levels of demand that maximizes (a) total revenue, and (b) profit for this product.

Explanation / Answer

I am going to assume that the 0.75 is supposed to be an exponent because otherwise, you would have multiplied it with 0.08. In the future, please use the ^ symbol to denote exponents. p=88.5-0.08Q^0.75 c=40000+40Q A) Find max revenue by setting MR=0. R=pQ R=(88.5-0.08Q^0.75)Q R=88.5Q-0.08Q^1.75 MR=88.5-0.14Q^0.75=0 88.5=0.14Q^0.75 Q=(88.5/0.14)^(1/0.75) Q=5425.257 B) Find max profit by setting MR=MC MR=88.5-0.14Q^0.75 c=40000+40Q MC=40 MR=88.5-0.14Q^0.75=40 0.14Q^0.75=48.5 Q=(48.5/0.14)^(1/0.75) Q=2433.053

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