As the new owner of a supermarket, you have inherited a large inventory of unsold imported Limburger cheese, and you would like to set the price so that your revenue from selling it is as large as possible. Previous sales figures of the cheese are shown in the following table. Price per Pound, p $3.00 $4.00 $5.00 Monthly Sales, q (pounds) 404 286 224 (a) Use the sales figures for the prices $4 and $5 per pound to construct a demand function of the form q = Ae-bp, where A and b are constants you must determine. (Round A and b to two significant digits.) q = (b) Use your demand function to find the price elasticity of demand at each of the prices listed. (Round your answers to two decimal places.) p = $3 E = p = $4 E = p = $5 E = (c) At what price should you sell the cheese to maximize monthly revenue? (Round your answer to the nearest cent.)
As the new owner of a supermarket, you have inherited a large inventory of unsold imported Limburger cheese, and you would like to set the price so that your revenue from selling it is as large as possible. Previous sales figures of the cheese are shown in the following table. Price per Pound, p $3.00 $4.00 $5.00 Monthly Sales, q (pounds) 404 286 224 (a) Use the sales figures for the prices $4 and $5 per pound to construct a demand function of the form q = Ae-bp, where A and b are constants you must determine. (Round A and b to two significant digits.) q = (b) Use your demand function to find the price elasticity of demand at each of the prices listed. (Round your answers to two decimal places.) p = $3 E = p = $4 E = p = $5 E = (c) At what price should you sell the cheese to maximize monthly revenue? (Round your answer to the nearest cent.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:As the new owner of a supermarket, you have inherited a large inventory of unsold imported Limburger cheese, and you would like to set the price so that your revenue from
selling it is as large as possible. Previous sales figures of the cheese are shown in the following table.
Price per Pound, p
$3.00
$4.00
$5.00
Monthly Sales, q (pounds)
404
286
224
Ae-DP, where A and b are constants you must determine.
(a) Use the sales figures for the prices $4 and $5 per pound to construct a demand function of the form q
(Round A and b to two significant digits.)
q =
(b) Use your demand function to find the price elasticity of demand at each of the prices listed. (Round your answers to two decimal places.)
p =
$3
E =
p = $4
E =
p = $5
E =
(c) At what price should you sell the cheese to maximize monthly revenue? (Round your answer to the nearest cent.)
$
(d) If your total inventory of cheese amounts to only 200 pounds and it will spoil one month from now, how should you price it to receive the greatest revenue? (Round
your answer to the nearest cent.)
Is this the same answer you got in part (c)? If not, give a brief explanation.
It is a higher price than in part (c) because at a lower price, you cannot satisfy the demand.
It is a lower price than in part (c) because at a higher price, the demand is not high enough.
It is the same price.
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