units of labor costs and units of metal costs
.
Thus total cost is ; this can
be at most . So our problem is
to
We form Lagrangian:
The partial derivatives are
First order conditions and complimentary slackness require
Solving the first two equations, we get
. Since can take only
non-negative values, we conclude from
that
can not be zero. Hence, from
we conclude that .
Using
we get
which implies . Therefore,
from
we get
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100
maximize 2x + 2ry+y subject to 3r +2y< 100
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OL =2x + 1 + 26,
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6(3x + 2y-100) = 0
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1.5-3b-2-3b-100 6b-103.5 > -6b103.5
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