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Find the maximum value of x 2 y subject to the constraint: x+y+(2x 2 +2xy+3y 2 ) 1/2 =k where k is a constant and x,y>=0

Find the maximum value of  x2y subject to the constraint:


x+y+(2x2+2xy+3y2)1/2 =k     where k is a constant and x,y>=0

Grade:12

1 Answers

askIITIians Expert
21 Points
15 years ago

 

Given,

x+y+(2x2 + 2xy + 3y2 )1/2 = k

x,y >= 0

Dear Student,

First write the above relation seperating y on one side and then substituting it in the equation.

z = x2y

1. Find dy/dx

2. Equate it to zero and get the value of x.

3. Then find d2y/dx2 & substitute the values of x from Step (2) in d2y/dx2  

4. If d2y/dx2   is -ve, it is maxima.

5. Substitute that value of y in the function, f = x2 y , you get the maximum value.

 

 

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