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Homework Help: Maximum Profit

  1. Sep 6, 2010 #1
    1. The problem statement, all variables and given/known data

    A company can do 300 units per week at a weekly cost per unit of $58 for labor and supplies. If the charge is $100 per unit, then it would have clients for 300 units. However, for each $5 price increase, it could expect to have 10 fewer units.

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 6, 2010 #2
    Can you come up with a formula for profit?

    Let's do the easy one first, when the company doesn't charge anything extra:
    Pi(x) = (number of units)(sell price - cost) = 300(100-58)
    Fairly straight forward, now let's modify this with a variable “x” which will represent how many times they will charge an extra $5.

    P(x) = (number of units)(sell price - cost) = (300-10x)(100+5x-58) = (300-10x)(42+5x)
    Now what we do from here depends on what class you are in. If you are in an algebra course, you should recognize this as a parabola and know how to graph it. If you are in calculus I would expand it, take the derivative, and set it equal to zero.
     
  4. Sep 7, 2010 #3
    Thanks for your help so far. I am in Precalculus. I need to plug these formulas into an excel spreadsheet.
     
  5. Sep 7, 2010 #4
    I have the formulas in the spread sheet. I think all is going well. I need to know what type of rule is this. I would really like to be able to figure this out. Is it the product of two polynomials?
     
  6. Sep 7, 2010 #5
    It is two polynomials multiplied. You should be able to do this by hand by using the FOIL method then putting it standard form for a parabola. Picture a parabola, what point would be the max or min?
     
    Last edited: Sep 7, 2010
  7. Sep 8, 2010 #6
    Thanks alot!
     
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