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The manager of a large apartment complex knows from experience that 120 units will be occupied if the rent is 468 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 6 dollar increase in rent. Similarly, one additional unit will be occupied for each 6 dollar decrease in rent. (a) If æ is the number of units rented, and p is the rent per unit in dollars, what is the price-demand equation (assuming it is linear)? p = (b) What is the monthly revenue function for the manager? (Hint: Revenue is the product of the price per item and the number of items.) R(x) = (c) How many apartment units should be rented to maximize the monthly revenue? apartment units (d) What is the maximum monthly revenue for the manager? Round your answer to the nearest cent if necessary. dollars (e) What rent should the manager charge to maximize the monthly revenue? Round your answer to the nearest cent if necessar

The manager of a large apartment complex knows from experience that 120 units will be occupied if the rent is 468 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 6 dollar increase in rent. Similarly, one additional unit will be occupied for each 6 dollar decrease in rent. (a) If æ is the number of units rented, and p is the rent per unit in dollars, what is the price-demand equation (assuming it is linear)? p = (b) What is the monthly revenue function for the manager? (Hint: Revenue is the product of the price per item and the number of items.) R(x) = (c) How many apartment units should be rented to maximize the monthly revenue? apartment units (d) What is the maximum monthly revenue for the manager? Round your answer to the nearest cent if necessary. dollars (e) What rent should the manager charge to maximize the monthly revenue? Round your answer to the nearest cent if necessar

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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The manager of a large apartment complex knows from experience that 120 units will be occupied if the rent is 468 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 6 dollar increase in rent. Similarly, one additional unit will be occupied for each 6 dollar decrease in rent. (a) If æ is the number of units rented, and p is the rent per unit in dollars, what is the price-demand equation (assuming it is linear)? p = (b) What is the monthly revenue function for the manager? (Hint: Revenue is the product of the price per item and the number of items.) R(x) = (c) How many apartment units should be rented to maximize the monthly revenue? apartment units (d) What is the maximum monthly revenue for the manager? Round your answer to the nearest cent if necessary. dollars (e) What rent should the manager charge to maximize the monthly revenue? Round your answer to the nearest cent if necessary. dollars per unit
Transcribed Image Text:The manager of a large apartment complex knows from experience that 120 units will be occupied if the rent is 468 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 6 dollar increase in rent. Similarly, one additional unit will be occupied for each 6 dollar decrease in rent. (a) If æ is the number of units rented, and p is the rent per unit in dollars, what is the price-demand equation (assuming it is linear)? p = (b) What is the monthly revenue function for the manager? (Hint: Revenue is the product of the price per item and the number of items.) R(x) = (c) How many apartment units should be rented to maximize the monthly revenue? apartment units (d) What is the maximum monthly revenue for the manager? Round your answer to the nearest cent if necessary. dollars (e) What rent should the manager charge to maximize the monthly revenue? Round your answer to the nearest cent if necessary. dollars per unit
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