SOLUTION: Find two positive numbers whose sume of the first and three times the second is 72 and whose product is a maximum?

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Question 439746: Find two positive numbers whose sume of the first and three times the second is 72 and whose product is a maximum?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Find two positive numbers whose sum of the first and three times the second is 72
and whose product is a maximum?
:
x + 3y = 72
x = (72-3y)
:
xy = the product, therefore:
f(y) = y(72-3y)
f(y) = -3y^2 + 72y
Find the axis of symmetry to find the max
y = %28-72%29%2F%282%2A-3%29
y = +12 is one number
:
Find the maximum
f(y) = -3(12^2) + 72(12)
f(y) = -432 + 864
f(y) = +432 is the max
then
x = (72-3(12))
x = 36 is the other number
:
:
Check by finding the product: 12 * 36 = 432