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Home Q & A Board Science-Related Homework Help Mathematics
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flowerxgurl flowerxgurl
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10 years ago
Find positive numbers x and y whose sum is 75 and for which the value of xy^2 is as large as possible
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#1
10 years ago
Y is 38, X is 37.

38 + 37 = 75
38^2 = 1444

1444 * 37 = 53428
wrote...
#2
10 years ago
Hi flowerxgurl,

Let R be the maximized product of xy^2
xy^2 = R

x + y = 75
y = 75 -x

plug in the other equation
x( 75-x)^2 = R
differentiate
(75-x)^2 + 2x(75-x)(-1) = 0
factor (75-x) out
(75-x)(75-x + -2x) = 0
(75-x)(75-3x) = 0
(75-x)*3(25-x) = 0
Rightwards Arrow x = 75,25

if x = 75, then R = 0
if x = 25, then R = 25*(75-25)^2
         R = 25*50^2 = 62500
Therefore, your R minimum is x = 75, y =0
      your R maximum is x = 25, y =50

My calculus is a bit rusty,
Hope this makes sense to you,
Laser
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