EXAMPLE 6 A store has been selling 200 Blu-ray disc players a week at $550 each. A market survey indicates that for each $10 rebate offered to buyers, the number of units sold will increase by 20 a week. Find the demand function and the revenue function. How large a rebate should the store offer to maximize its revenue? SOLUTION If x is the number of Blu-ray players sold per week, then the weekly increase in sales is For each increase of 20 units sold, the price is decreased by $10. So for each additional unit sold, the 1 x 10 and the demand function is 20 decrease in price will be p(x) = 550 (x – 200) = 650 – %3D The revenue function is R(x) = xp(x) = Since R'(x) = we see that R'(x) = 0 when x = This value of x gives an absolute maximum by the First Derivative Test (or simply by observing that the graph of R is a parabola that opens downward). The corresponding price is p(650) = and the rebate is 550 – 325 = Therefore, to maximize revenue, the - store should offer a rebate of $

EXAMPLE 6 A store has been selling 200 Blu-ray disc players a week at $550 each. A market survey indicates that for each $10 rebate offered to buyers, the number of units sold will increase by 20 a week. Find the demand function and the revenue function. How large a rebate should the store offer to maximize its revenue? SOLUTION If x is the number of Blu-ray players sold per week, then the weekly increase in sales is For each increase of 20 units sold, the price is decreased by $10. So for each additional unit sold, the 1 x 10 and the demand function is 20 decrease in price will be p(x) = 550 (x – 200) = 650 – %3D The revenue function is R(x) = xp(x) = Since R'(x) = we see that R'(x) = 0 when x = This value of x gives an absolute maximum by the First Derivative Test (or simply by observing that the graph of R is a parabola that opens downward). The corresponding price is p(650) = and the rebate is 550 – 325 = Therefore, to maximize revenue, the - store should offer a rebate of $

Intermediate Algebra

19th Edition

ISBN:9780998625720

Author:Lynn Marecek

Publisher:Lynn Marecek

Chapter4: Systems Of Linear Equations

Section4.3: Solve Mixture Applications With Systems Of Equations

Problem 158E: The manufacturer of an energy drink spends $1.20 to make each drink and sells them for $2. The...

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