Question

1.    Given the utility function of the form: U (x, y) = 4x² + 3xy + 6y²: maximize utility subject to the budget constraint: x + y = 56. Then find the utility maximizing level of output x and y?

Answer 1

$$Lag=4x^2+3xy+6y^2-\lambda(x+y-56)$$

$$\frac{\varDelta Lag}{\varDelta x}=8x+3y-\lambda$$

$$\frac{\varDelta Lag}{\varDelta y}=3x+12y-\lambda$$

$$y=1.8x$$

$$x=31$$

$$y=56$$