2. A real estate agency manages a building with 100 units and charges a base rent of $720 per month for each unit. At this base rent all 100 units will be occupied. Experience has shown that for each increase in the rent of all units by $10 per month one unit will become vacant (i.e. if the rent was raised by $10 twice to $740 then two units would become vacant so only 98 would be occupied). The monthly cost of maintaining each rented unit is $20. The agency is allowed to charge at most $900 per unit. (a) What rent should the agency charge in order to maximise its profit? (b) What is the difference between the number of units occupied when the profit is a maximum compared to when the profit is a minimum?
2. A real estate agency manages a building with 100 units and charges a base rent of $720 per month for each unit. At this base rent all 100 units will be occupied. Experience has shown that for each increase in the rent of all units by $10 per month one unit will become vacant (i.e. if the rent was raised by $10 twice to $740 then two units would become vacant so only 98 would be occupied). The monthly cost of maintaining each rented unit is $20. The agency is allowed to charge at most $900 per unit. (a) What rent should the agency charge in order to maximise its profit? (b) What is the difference between the number of units occupied when the profit is a maximum compared to when the profit is a minimum?
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:2. A real estate agency manages a building with 100 units and charges
a base rent of $720 per month for each unit. At this base rent all 100
units will be occupied. Experience has shown that for each increase
in the rent of all units by $10 per month one unit will become vacant
(i.e. if the rent was raised by $10 twice to $740 then two units would
become vacant so only 98 would be occupied). The monthly cost of
maintaining each rented unit is $20. The agency is allowed to charge
at most $900 per unit.
(a) What rent should the agency charge in order to maximise its
profit?
(b) What is the difference between the number of units occupied
when the profit is a maximum compared to when the profit is a
minimum?
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