You have been hired to consult at a publishing company and you have been approac

Question

You have been hired to consult at a publishing company and you have been approached to determine the best selling price for a new Calculus text. You decide to make life easy and assume that the demand equation for the text has a linear form.

a) Your market studies reveal that when the price is set at $50.00 per book, the sales amount to 10,000 per year. When the price is $80.00 per book, the sales drop to 1000 per year. Use this information to find the demand equation

b) Now find the unit price that maximizes the annual revenue and predict what the publishing company's revenue will be at that price.

Explanation / Answer

(a) With a price increase of $30, the number of sales drops by 9,000. This means that per dollar of price increase, the sales drop by 9000/30 = 300 units. Therefore, we get the equation D = 25000 - 300P. (b) The equation for revenue is (25000 - 300P)P = 25000P - 300P^2. We take the derivative and set it equal to 0 to get 25000 - 600P = 0, so the optimal price is P = 25000/600 = 125/3 = $41.67. At this price, the revenue is (25000 - 300*125/3)*125/3 = $520,833.33

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.