The manager of a large apartment complex knows from experience that 100 units will be occupied if the rent is 490 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 7 dollar increase in rent. Similarly, one additional unit will be occupied for each 7 dollar decrease in rent. (a) If z 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= 490 + 7x (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(z) = 4900 +210x-7x (c) How many apartment units should be rented to maximize the monthly revenue? 15 apartment units
The manager of a large apartment complex knows from experience that 100 units will be occupied if the rent is 490 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 7 dollar increase in rent. Similarly, one additional unit will be occupied for each 7 dollar decrease in rent. (a) If z 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= 490 + 7x (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(z) = 4900 +210x-7x (c) How many apartment units should be rented to maximize the monthly revenue? 15 apartment units
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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Step 1: Given
VIEWStep 2: a) Find price demand equation.
VIEWStep 3: b) Obtain monthly revenue function
VIEWStep 4: c) Find the number of units that has to be rented such that revenue is maximum
VIEWStep 5: d) Find the Maximum revenue
VIEWStep 6: e) Obtain the rent such that revenue is maximum
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