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Homework Help: Maximizing profit equation

  1. Mar 30, 2010 #1
    Maximizing profit equation URGENT

    1. The problem statement, all variables and given/known data:
    A goat salesman can sell 12 goats per day at a price of 15000 each. His marketing dept estimates that for each $300 price reduction he can sell 2 more goats per day. If each goat costs him $12000, and fixed costs are $1000, use calculus to determine what price he should charge to maximize his profit? How many goats will he sell at this price? (hint! Let x be the number of $300 price reductions.)



    2. Relevant equations:

    ?

    3. The attempt at a solution:

    I started off with p-15000= [(15000-300)/(12-14)] (x-12)

    which, after deriving and equating p' to 0 ; i got x= 7.02




    My issue:

    I honestly dont think i got the first equation right. I've tried thinkin outside the box on this one, but i have a feeling that its much easier than im making it out to be in my own head. This problem is for a group assignment and I can't let my group down. I asked my math tutor, but shes totally useless for application problems involving business.




    Thank you to anyone for any help/ attempting to help :) :)

    ps. i would usually find a more competent tutor or ask my school's tutor, but its crunch time on the day before the group thing is due, so im kinda stuck between a rock and this math problem.
     
  2. jcsd
  3. Mar 30, 2010 #2

    Dick

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    Re: Maximizing profit equation URGENT

    Break the problem down into parts and express each as a function of x. i) how many goats do you sell per day and ii) what's the price of each goat. Try to combine those into an expression with the other facts to get an expression for profit.
     
  4. Mar 30, 2010 #3
    Re: Maximizing profit equation URGENT

    express each as a function of the number of price reductions? Is that what you are saying? or just x as a variable
     
  5. Mar 30, 2010 #4

    Dick

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    Re: Maximizing profit equation URGENT

    Yes, x as the number of price reductions. Follow the hint. "just x as a variable" doesn't mean much. So answer my questions i) and ii).
     
  6. Mar 30, 2010 #5
    Re: Maximizing profit equation URGENT

    This is probably a very easy easy question, but im kinda stumped on how to figure it out. even your Q's i) and ii), Dick, please excuse my stupidity, i just wanna solve it so my group doesnt take a fall.
     
  7. Mar 30, 2010 #6

    Dick

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    Re: Maximizing profit equation URGENT

    You can't figure out an expression for number of goats sold per day if x is the number of price reductions?? The only way not to let your group down is to figure this out. Let's call that expression GPD. If x=0, the GPD=12. If x=1, then GPD=14. If x=2, then GPD=16. This is easy.
     
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