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Word problem, finding maximum

  1. Oct 14, 2008 #1
    1. The problem statement, all variables and given/known data

    Find two numbers whose product is a maximum if the sum of the first number and twice the second is 100

    2. Relevant equations

    3. The attempt at a solution

    Alright so I think I might have the right answer but something just doesn't seem right.

    so first I named my two variables x,y then I set up the problem in terms of x and y


    then I solved for y to get


    then I multiply the new y value and x to get the maximum

    x(50-x/2)=0 solve to get


    so then I plug my x value back in to get my y value and end up with

    (25/2,175/4) as my maximum right?
  2. jcsd
  3. Oct 14, 2008 #2
    oh wait so I found the answer in my text book (the original question was on a lab but my teachers almost all the lab questions from the book) and the answer is 50 and 25 which makes sense but i still can't find the flaw in my logic : (
    Last edited: Oct 14, 2008
  4. Oct 14, 2008 #3


    User Avatar
    Homework Helper

    Why do you set

    x\left(50 - \frac x 2 \right)

    equal to zero and solve for [tex] x [/tex]? You don't want this product to be zero, you want it
    to be the maximum value possible. That is where your error lies.
  5. Oct 14, 2008 #4
    oh yeah, you're right. :blushing:
  6. Oct 14, 2008 #5


    Staff: Mentor

    You determined that the two numbers are x and 50 - x/2.

    Let's get rid of y as you first defined it (i.e., as the other number, which you've already figured out) and let's now use it to represent the product of the two numbers.

    So y = x(50 - x/2)

    If you think of the graph that the equation above represents, what you found is where that graph crosses the x-axis. You found one of these points and missed the other one.

    Is there a high point for this graph? That's really what you're looking for, not where the graph crosses the x-axis.
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