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Multivariable Calculus

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Lagrange Multipliers: Find maximum of $x{ e }^{ y }$

MVCALC-BJVZSD

Use the method of Lagrange Multipliers to maximise $x{ e }^{ y }$ subject to the constraint $2x+y=10$.

At what point $(x,y)$ is the maximum attained?

A

$(3,4)$

B

$(\frac { 1 }{ 2 } ,9)$

C

$(4,2)$

D

$(\frac { 10 }{ 3 } ,\frac { 10 }{ 3 } )$