Question

The manager of a large apartment complex knows from experience that 120 units will be occupied if the rent is 342 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 9 dollar increase in rent. Similarly, one additional unit will be occupied for each 9 dollar decrease in rent. What rent should the manager charge to maximize revenue

Answer 1

Answer:

The answer is "711"

Explanation:

Calculated equation:

$R(x) =(120-x)(342+9x)\\\\R(x) =-9x^2+738x+41040$

For maximum revenue $R'(x)=0$

$\to R'(x) =-18x+738\\\\\to 18x=738\\\\\to x=\frac{738}{18}\\\\\to x=41$

So, maximum revenue:

$\to 342+9\times 41\\\\\to 342+369\\\\\to 711$