Word problem, finding maximum

  • Thread starter Geekchick
  • Start date
  • #1
74
0

Homework Statement



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

Homework Equations





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

x+2y=100

then I solved for y to get

y=50-x/2

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

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

x=25/2

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?
 

Answers and Replies

  • #2
74
0
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:
  • #3
statdad
Homework Helper
1,495
36
Why do you set

[tex]
x\left(50 - \frac x 2 \right)
[/tex]

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.
 
  • #4
74
0
oh yeah, you're right. :blushing:
 
  • #5
35,393
7,271

Homework Statement



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

Related Threads on Word problem, finding maximum

Replies
1
Views
9K
  • Last Post
Replies
0
Views
929
Replies
2
Views
2K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
17
Views
2K
  • Last Post
Replies
1
Views
796
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
7
Views
2K
Replies
1
Views
1K
Top