-Find two positive numbers satisfying the given requirements:

The sum of the first and twice the second is 80 and the product is a maximum.

1 answer

a +2 b = 80 so a = 80 - 2 b
y = a b so y = (80-2 b)b = 80 b - 2 b^2
dy/db = 80 - 4 b
= 0 for max or min
4 b = 80
b = 20
then a = 40
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