The manager of a large apartment complex knows from experience that 110 units wi

Question

The manager of a large apartment complex knows from experience that 110 units will be occupied if the rent is 460 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 10 dollar increase in rent. Similarly, one additional unit will be occupied for each 10 dollar decrease in rent. What rent should the manager charge to maximize revenue?

I have tried multiplying out and finding the derrivatvie etc. keep getting x= -32. Answered 428, 140, 600: all wrong. Not sure what I am missing.

Explanation / Answer

suppose rent is 460+10x

so occupancy = 110-x

so Revenue=R=(460+10x)*(110-x)

R'=1100-10x-460-10x=640-20x=0 at x=32 and y''(32)=-ve (so max. exist)

So Rent must be 780

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