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 Question from a student: A real-estate firm owns 100 garden type apartments. At RM400 per month, each apartment can be rented. However, for each RM10 per month increase, there will be two vacancies with no possibility of filling them. What rent per apartment will maximize monthly revenue?

Hi,

The revenue each month is the rent charged per unit times the number of units rented.

Suppose the monthly increase per unit is $RMx,$ then each unit pays $RM(400 + x).$ For each RM10 increase in rent there are 2 vacancies. Hence if the rent increases by $RMx$ there are $2\times \large \frac{x}{10}$ vacancies and hence the number of units rented is $100 - 2\times \large \frac{x}{10}.$

Now use the calculus you know to determine the value of $x$ that will maximize the monthly revenue.

Penny

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