A nursery sells grass seed A for $6.75 per pound and grass seed B for $5.50 per pound. The nursery sells a mixture of the two ki
nds of seeds for $6.25 per pound. Let x represent the amount of seed A the nursery uses in 5 pound of the mixture.
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Let 
be the solid. Then the volume is
which follows from the facts that
(by computing the Jacobian)
and
(we take the positive solution, since it's clear that lies above the 
-
plane)
(again, taking the positive root for the same reason)
which follows from the facts that
(by computing the Jacobian)
and
(we take the positive solution, since it's clear that
(again, taking the positive root for the same reason)