After school Philippe spent 1 3/4 hours at baseball practice, 2 1/4 hours on homework, and 1/4 hour getting ready for bed. About
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Given 
subject to the constraint 
Let
.
The gradient vectors of
and 
are:
and 
By Lagrange's theorem, there is a number
, such that
It can be seen that has local extreme values at the given region.
Let
The gradient vectors of
By Lagrange's theorem, there is a number
It can be seen that