SOLUTION: Find the maximum product of two numbers whose sum is 60. Is there a minimum product? Explain.

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Question 1106230: Find the maximum product of two numbers whose sum is 60. Is there a minimum product? Explain.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
A%2BB=60
So then what is the maximum of Z=AB?
You can substitute from above,
A=60-B
So,
Z=%2860-B%29B
Z=60B-B%5E2
So find the maximum of Z.
Since there is a negative coefficient in front of the quadratic term, the parabola opens downward and has a maximum.
Since it's a parabola you can convert to vertex form and find the maximum and the location of the maximum.