Suppose that the utility function for two products is given by , and the budget constraint is . Find the values of x and y that maximize utility.
B)
C)
D)

Question

Suppose that the utility function for two products is given by  , and the budget constraint is  . Find the values of x and y that maximize utility. ​
B)​ 
C)​ 
D)​

Quizplus · Accepted Answer

We can solve for the Lagrange multiplier λ as follows:
L = x^2y - λ(4x + 3y - 240)
Taking partial derivatives with respect to x and y and setting them equal to 0:
2xy - 4λ = 0
x^2 - 3λ = 0
Solving these equations simultaneously, we get:
x = 2λ, y = 8λ/3
Substituting these values into the budget constraint, we get:
2(2λ) + 3(8λ/3) = 240
Simplifying, we get:
8λ + 8λ = 240
λ = 15
Therefore, x = 30 and y = 40 are the values that maximize utility.

Suppose That the Utility Function for Two Products Is Given