Calc

posted by .

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?

I was given the answer 46208 but that answer is incorrect. Can someone help me? Please

  • Calc -

    let the number of $8 increments be n

    so number occupied = 100-n
    cost per unit = 416+8n


    Revenue = R = (100-n)(416+8n)
    = 41600+ 800n - 416n - 8n^
    = 41600 + 384n - 8n^2

    dR/dn = 384 - 16n = 0 for a max of R
    16n = 384
    n = 24

    so the rent should be 416+8(24) = $608
    with 100 - 24 or 76 units rented for a max
    revenue of 76(608) or $46208

    The answer is correct for the max profit, but it asked for the rental cost to obtain that , which
    was $608 per unit.
    for a max revenue of
    41600 + 384(24) - 8(24)^2 or $

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    The manager of a large apartment complex knows from experience that 90 units will be occupied if the rent is 370 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 5 dollar …
  2. calculus

    The manager of a large apartment complex knows from experience that 100 units will be occupied if the rent is 350 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 7 dollar …
  3. Calculus

    The manager of a large apartment complex knows from experience that 80 units will be occupied if the rent is 472 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 4 dollar …
  4. Calculus

    The manager of a large apartment complex knows from experience that 80 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 …
  5. Calculus

    The manager of a large apartment complex knows from experience that 90 units will be occupied if the rent is 360 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 9 dollar …
  6. Calc Help Please

    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 …
  7. Calculus-Applied Optimization Problem

    The manager of a large apartment complex knows from experience that 100 units will be occupied if the rent is 425 dollars per month. A market survey suggests that, on average, one additional unit will remain vacant for each 9 dollar …
  8. Calculus: Help Me

    The manager of a large apartment complex knows from experience that 120 units will be occupied if the rent is 294 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 7 dollar …
  9. Calculus

    The manager of a large apartment complex knows from experience that 80 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 …
  10. Math 115

    The manager of a large apartment complex knows from experience that 90 units will be occupied if the rent is 444 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 6 dollar …

More Similar Questions