How do you optimize #f(x,y)=xy-x^2+e^y# subject to #x-y=8#?
1 Answer
Mar 1, 2016
Minimum of f(x, y) = f(3 ln 2 + 8, 3 ln 2 ).
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Explanation:
Substitute x = y + 8.
f(x, y) = g(y) = y(y + 8)
Necessary condition for g(y) to be either a maximum or a minimum is
The second derivative is e^y > 0, for all y. This is the sufficient condition that g(3 ln 2) is the minimum of g(y).