Question

For each of the following functions, use the Lagrange multiplier to find the critical values that 

will optimize functions subject to the given constraints and estimate by how much the objective 

functions will change as a result of 1 unit change in the constant of the constraint 

i) Maximize Z = 2x

2 

- xy + 3y

2 subject to x + y = 72 [5 Marks]

ii) Maximize f(x,y) = 26x – 3x

2 + 5xy – 6y

2 + 12y subject to 3x + y = 170 [5 Marks]

iii) Maximize f(x,y,z) = 16x2yz subject to x + y + z = 224 [5 Marks]

Answer 1

The answer to your question is provided below