The function f(x, y)equals=3 x plus 3 y 3 x+3y has an absolute maximum value and absolute minimum value subject to the constraint 9 x squared minus 9 xy plus 9 y squared equals 169 x 2−9xy+9y2=16. Use Lagrange multipliers to find these values.

Therefore the absolute maximum value is

the absolute minimum value is

Step-by-step explanation:

Method of Lagrange multipliers:

1. Solve the following system of equation

2. Plug the all solution (x,y,..) from the first step into f(x,y,..) and identify the maximum and minimum values.

The constant is known as the Lagrange Multiplier.

Given function is

f(x,y)= 3x+3y

subject to constrain

The partial derivatives are

......(1)

......(2)

.....(3)

Multiplying 2 with equation (2) and add with  equation (1)

Putting the value of y in equation (1)

Putting the value of x and y in equation (3)

Therefore the value of x and y becomes

and

Therefore

            =4+4

            =8

                =-4-4

                =-8

Therefore the absolute maximum value is

the absolute minimum value is

step-by-step explanation:

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step-by-step explanation: