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Optimization (I believe it's called) word problems

  1. Oct 6, 2011 #1
    1. The problem statement, all variables and given/known data
    A real estate company owns 180 apartments, which are fully occupied when the rent is $300. The company estimates that for each $10 increase in rent, 5 apartments will become unoccupied. What rent should be charged so that the company will receive the max income?



    2. Relevant equations
    x=-b/2a (in ax^2+bx+c)



    3. The attempt at a solution
    c=cost
    a=apartments
    d= 10 dollar increase in price

    c=300+d
    a=180-5d

    multiplying those together gets a nonsense negative (can't decrease the price, the apartments are full)
     
  2. jcsd
  3. Oct 6, 2011 #2

    Mark44

    Staff: Mentor

    Before trying to answer this question, see if you can figure out what the rental income will be for a few sets of values.

    For example, what is the total revenue when they charge $300 per apartment?
    What is the revenue if they raise the rent by $10?
    What is the revenue if they raise the rent by $20?

    After you get a feel for how this is working, we'll look at what happens when they raise the rent by $x.
     
  4. Oct 6, 2011 #3
    I all ready know what the answers is. It increases until 330 (30 dollars increase) and then begins to decrease. It's a parabola from 300 to 360. But I just can't find a way beyond trying numbers to solve it
     
  5. Oct 6, 2011 #4

    Mark44

    Staff: Mentor

    How do you know it's a parabola?
     
  6. Oct 6, 2011 #5

    eumyang

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    Homework Helper

    d isn't defined well, so the 1st equation (bolded) isn't correct. The way you wrote the equations, if d = 10, then a = 130, not 175. You'll need to rework the 1st equation.
     
  7. Oct 6, 2011 #6
    d is a 10 dollar increase. d=10 is a 100 dollar increase
     
  8. Oct 6, 2011 #7

    eumyang

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    Homework Helper

    But when you put d = 10 into the equation
    c = 300 + d,
    you get c = 310, not 400. :confused:
     
  9. Oct 6, 2011 #8
    so let's call d a one collar increase

    so c=300+10d

    what's the other equation then
     
  10. Oct 6, 2011 #9

    eumyang

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    Homework Helper

    I'd rather call d, "the number of $10 increases." So d = 10 means that there are 10 $10 increases, or a total increase of $100. Your 2nd equation (for a) is correct.
     
  11. Oct 6, 2011 #10
    so then how do I fix it to get a reasonable answer
     
  12. Oct 6, 2011 #11
    got it, I hope I understand the other ones now
     
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