SOLUTION: Find two numbers such that their product is as large as possible, given that two times the first number plus three times the second number is 60

Question 954660: Find two numbers such that their product is as large as possible, given that two times the first number plus
three times the second number is 60
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Let the two numbers be X and Y.
You want to maximize with .
From the second equation,

Substitute into the product,

Now the product is the function of only one variable.
You can either take the derivative and find the extrema or since it's a quadratic, you can convert it to vertex form to find the maximum.

In vertex form, the parabola opens downwards and the vertex value is the maximum.
The maximum occurs when
So then,

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