How do you solve these? Please include correct work and answers thank you. 1) Find the maximum value of
f(
x,
y) =
xysubject to
x+ 2
y=68.
fmax= Also find the corresponding point (
x,
y). (
x,
y) =
5.
/12 pointsWaneFMAC6 15.4.008.
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2)Use Lagrange multipliers to solve the given optimization problem. HINT [See Example 2.] Find the maximum value of
f(
x,
y) =
xysubject to 3
x+
y=66.
fmax= Also find the corresponding point (
x,
y). (
x,
y) =
6.
/15 pointsWaneFMAC6 15.4.009.
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3)Use Lagrange multipliers to solve the given optimization problem. HINT [See Example 2.] Find the maximum value of
f(
x,
y) = 4
xysubject to
x2+
y2=2.
fmax= Also find the corresponding points (
x,
y). (
x,
y) =
(smallerx-value) (
x,
y) =
(largerx-value) 7.
/14 pointsWaneFMAC6 15.4.010.
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4)Use Lagrange multipliers to solve the given optimization problem. HINT [See Example 2.] Find the maximum value of
f(
x,
y) =
xysubject to
y=3
x2.
fmax= Also find the corresponding point (
x,
y). (
x,
y) =
8.
/12 pointsWaneFMAC6 15.4.011.
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5)Use Lagrange multipliers to solve the given optimization problem. HINT [See Example 2.] Find the minimum value of
f(
x,
y) =
x2+
y2subject to
x+ 2
y=45.
fmin= Also find the corresponding point (
x,
y). (
x,
y) =
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