The business manager of a 90 unit apartment building is tryingto determine the rent to be charged. From past experience withsimilar buildings, when rent is set at $400, all the units arefull. For every $20 increase in rent, one additional unit remainsvacant. What rent should be charged for maximum total revenue? Whatis that maximum total revenue?
To help solve the above scenario, perform an internet search forProfit Parabola or Applications of Quadratic Functions. List theURL of one of the applications that you find.
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Go to http://www.purplemath.com/modules/quadprob3.htm to see theprocess used for determining the quadratic function for revenuesR(x) as a function of price hikes x on page 3 with thecanoe-rental business problem. Use this process to determine thequadratic function that models the revenues R(x) as a function ofprice hikes x in the apartment building scenario above.SHOW ALL YOUR WORK!
Rent hikes | Rent per apartment | Number of rentals | Total revenue |
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3. What is the formula for revenues R after x $20 price hikes in the apartment building?
Graph the function. Clearly label the graph (desmos.com is agreat an on-line graphing resource).
Find the maximum revenue (or income) of the apartmentbuilding.
What is the rent that coincides with this maximum revenue?
What is the outcome of the rent hike of $20 results in 2additional vacancies instead of 1 additional vacancy? Recalculatequestions 3, 5, 6 for this new scenario.
