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The manager of a large apartment complex knows from experience that 100 units will be occupied if the rent is 416 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 8 dollar increase in rent. Similarly, one additional unit will be occupied for each 8 dollar decrease in rent. What rent should the manager charge to maximize revenue?

revenue = # units * rent/unit
If each unit is rented for x,

r = x (100-(x-416)/8)
dr/dx = 152 - x/4
dr/dx=0 when x = 608

so, max rent is 608*76 = 46208

If you had read the whole explanation, you would have seen that the answer of rent=608 was given. Sorry for giving you more than you needed.

You could have saved reposting it and looking clueless.

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