Answer the following:

Part 2: Constrained optimization (50 points). The utility Maria gets from consuming cookies (x1) and cakes (X2) is defined by the function: U(X1,, X2) = x4xt 1 3 1 2 Cookies cost PhP25 per piece, while cakes cost PhP40 per slice. a. Suppose she intends to reach a level of utility of 50 units, how many cookies and slices of cake should she buy? How much should she spend on cookies and cake? (30 pts) Note: No need to derive the second order condition b. What would be her total spending (5 pts)? c. Using the envelope theorem (no need to show the proof for the envelope theorem), solve for the change in Maria's optimal spending if: i. Cake becomes more expensive by PhP5 (5 pts) ii. Cookies becomes cheaper by Php5 (5 pts) iii. Target utility increases by 10 units (5 pts)