Calculus/calculus

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Question
The manager of a luxury condominium complex in Tanjung Bungah know from experience that all 200 units will be occupied if the rent is RM500 per week. A market survey shows that averagely one additional unit will remain vacant for each RM 20 increase in rent. What rent should the manager charge to maximize the rent collections? determine the number of unit to be rent out and the maximum revenue obtained?

Answer
Let the number of units remaining vacant as a result of the rent hike be x.

Then the rental price per unit would be 500+20x

Total number of occupied units as a result of the above would be equivalent to 200-x

Hence, total revenue obtained = number of units rented out * rental price per unit


R = ( 200-x) *(500+20x)

 = 100000 + 3500x - 20x^2

When maximum revenue is obtained, dR/dx=0

ie  3500 - 40x =0

x=87.5

Assuming only full units are rented out, then the manager would be indifferent between accepting x=87 and x=88

As such, for x=87, he would charge 500+20(87)=RM 2240

and total revenue would be (200 -87) * 2240 =RM 253120  

For x=88, he would charge 500+20(88)=RM 2260

However, the total revenue would still be = (200 -88) * 2260 =RM 253120    (shown)

Hope this helps. Peace.

Calculus

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Frederick Koh

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I can answer questions concerning calculus, complex numbers, vectors, statistics , algebra and trigonometry for the O level, A level and 1st/2nd year college math/engineering student.

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More than 7 years of experience helping out in various homework forums. Latest Presence is over at http://www.thestudentroom.co.uk/ . You can also visit my main maths website http://www.whitegroupmaths.com where I have designed "question locker" vaults to store tons of fully worked math problems. A second one is currently being built. Peace.

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