5. (8 points) Haleys utility function is U = 4X2Y2, where X = veggie burgers per week and Y = cans of coke per week. Her weekly income is $90, the price of a veggie burger is $5, and that of a can of coke is $1 (assume veggie burger is on the x-axis).

i. State Haleys problem mathematically: (2 points)

- Objective:

- Constraint: ii. Provide the Lagrange function for the above problem: (1 points)

iii. Provide the first order conditions: (3 points)

iv. If MRS = Y/X and price ratio Px/Py = 5/1, how many burgers and cans of coke are consumed by Haley to maximize her utility? (2 points)