Question #10 In Exercises 7-18, use Lagrange multipliers to solve the given opti

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Question #10

In Exercises 7-18, use Lagrange multipliers to solve the given optimization problem. Find the maximum value of f(x, y) = xy subject to x + 2y = 40. Also find the corresponding point(s) (x, y) Find the maximum value of f(x, y) = xy subject to 3x + y = 60. Also find the corresponding point (s) (x, y) Find the maximum value of f (x, y) = 4xy subject to x^2 + y^2 = 8. Also find the corresponding point(s) (x y) Find the maximum value of f(x, y) = xy subject to y = 3 - x^2. Also find the corresponding point(s) (x y)

Explanation / Answer

let f(x,y)=xy and g(x,y)=x+2y

then use lagrange multiplier

then difreentiate function f(x,y) with respect to x and y

we will get fx=kgx and fy=kgy where k is lagrange multiplier and gx represent difrrentiation of g(x,y) w.r.t x

solving this function value you will get k=10

hence point will be x=20 and y=10

therefore f(x,y)max=20*10=200 answer

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