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

Respuesta :

Answer:

The answer is "711"

Explanation:

Calculated equation:

[tex]R(x) =(120-x)(342+9x)\\\\R(x) =-9x^2+738x+41040[/tex]

For maximum revenue [tex]R'(x)=0[/tex]

[tex]\to R'(x) =-18x+738\\\\\to 18x=738\\\\\to x=\frac{738}{18}\\\\\to x=41\\\\[/tex]

So, maximum revenue:

[tex]\to 342+9\times 41\\\\\to 342+369\\\\\to 711[/tex]

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