1. Maximize utility when the utility function is u(x,y)= xy+x, subject to the bu

Question

1. Maximize utility when the utility function is u(x,y)= xy+x, subject to the budget constraint, 6x+ 2y =110 Check that utility is , indeed, maximized. 2. Maximize utility when the utility function is u(x,y) =x0.5y0.5, subject to the budget constraint 4x + 6y = 130. Check that utility is, indeed, maximized. In addition, given an economic interpretation of the Lagrange multiplier () 3. Minimize the function f (x,y) = 3x2 +5xy +6y2, subject to the constraint 5x +7y =732. Check that the function is , indeed, minimized.

Explanation / Answer

u(x,y)= xy+x,

subject to the budget constraint,

6x+ 2y =110

solving we get

x = 28/3 , y = 27

U = 261.3333

2)

x = 16.25 , y = 10.83333

U = 13.26807

3)

x = 75 , y = 51

U = 51606

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