SOLUTION: Two positive numbers x and y are related by 2x+y=60. (a) Find a function that models the sum of the square of x and y. (b) Find the values of x and y that minimize the function.

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Question 847879: Two positive numbers x and y are related by 2x+y=60.
(a) Find a function that models the sum of the square of x and y.
(b) Find the values of x and y that minimize the function.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
2x%2By=60
y=60-2x
f=x%5E2%2By%5E2
f=x%5E2%2B%2860-2x%29%5E2
f=x%5E2%2B3600-240x%2B4x%5E2
f=5x%5E2-240x%2B3600
Find the derivative and set it equal to zero.
df%2Fdx=10x-240=0
x=24
y=60-2%2824%29=12
f=24%5E2%2B12%5E2=720