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For each of the following functions, find the extreme value of z (this can be either...

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Advance Math

For each of the following functions, find the extreme value of z(this can be either max or min), subject to a given constraint bythe method of direct substitution.

(a) z = xy, subject to the constraint x2 +y2 = 16 (Note that there are four solutions.)

(b) z = 3x2 − 10xy + 12y2 , subject to theconstraint y = 20 − 1/2 x

(c) z = xy, subject to the constraint x − y = 2

(d) z = x2 + y, subject to the constraint x/y = 2

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