Question

The manager of a 150-unit apartment building knows from experience that all the units will be occupied if the rent is $1,000 per month. A market survey suggests that, on average, one additional unit will remain vacant for each $20 increase in rent. Answer the following questions, following the precise requests (free-lancing will be considered a mistake). 1. Find a function that gives the number of units occupied N as a function of the rent charged, x, in dollars. Write an explicit formula for the function N(x). 2. Find a function that gives the revenue in dollars as a function of the rent charged. Calling the revenue R, you have to write an explicit formula for the function R(x). 3. What rent should the manager charge to maximize the revenue?

          The manager of a 150-unit apartment building knows from experience that all the units will be occupied if the rent is $1,000 per month. A market survey suggests that, on average, one additional unit will remain vacant for each $20 increase in rent. Answer the following questions, following the precise requests (free-lancing will be considered a mistake).
1. Find a function that gives the number of units occupied N as a function of the rent charged, x, in dollars. Write an explicit formula for the function N(x).
2. Find a function that gives the revenue in dollars as a function of the rent charged. Calling the revenue R, you have to write an explicit formula for the function R(x).
3. What rent should the manager charge to maximize the revenue?

The manager of a 150-unit apartment building knows from experience that all the units will be occupied if the rent is 1,000 per month. A market survey suggests that, on average, one additional unit will remain vacant for each20 increase in rent. Answer the following questions, following the precise requests (free-lancing will be considered a mistake).
1. Find a function that gives the number of units occupied N as a function of the rent charged, x, in dollars. Write an explicit formula for the function N(x).
2. Find a function that gives the revenue in dollars as a function of the rent charged. Calling the revenue R, you have to write an explicit formula for the function R(x).
3. What rent should the manager charge to maximize the revenue?

Added by Larry L.

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