You and your roommate go to the movies. You have a $10 gift card to spend on soda and popcorn. Since it is a gift card, it is in your best interest to spend all of it. Let ? denote the quantity of soda that you buy and ? the quantity of popcorn. Your utility is given by:

You and your roommate go to the movies. You have a $10 gift card to Spend on soda and popcorn. Since it is a gift card, it is in your best interest to spend all of it. Let S denote the quantity of soda that you buy and P the quantity of popcorn. Your utility is given by: U(S, P) = sari-a. The price of soda is p5 = $1 per unit, the price of popcorn is pp = $2, and the parameter a = 0.5. Your utility maximization problem is thus given by: maxS'rPH' S,P subject to p55 + pPP 5 10. To solve this problem, we will use Excel's Solver tool to numerically compute the optimal choice of S and P. The three key ingredients to any Solver optimization problem are: 1. The target cell = Our objective function (U(S, P) = S'IPH') 2. The changing cell(s) = Our choice variables (S, P) 3. The constraints = [psS + ch s 10] What is the optimal quantity of popcorn and soda for you to buy? What fraction of your budget do you spend on popcorn? The Excel template for the exercise will help you get started. Para meters alpha p_S p_P Money to spend NOTES: Utility function parameter (no units) Price of soda (in dollars) Price of popcorn (in dollars) Money on gift card (in dollars) The choice variables (S and P) |:l Hint: These variables are endogenous; put a plausible guess for an answer in these cells before you start; this helps the solver get started Quantity of soda (5) Quantity of popcorn (P) The (budget) constraint Total expenditure This cell will be part of your constraint; you have to f ill it with a formula before you run the solver The target cell: obj ective to maximize You need a formula in this cell before you start. You might also find it helpful to put the cursor here before clicking the "Solver" button to get started If you can't find Solver, you may need to add it throu h "Excel Add Ins...Il What is the optimal quantity of popcorn and soda for you to buy? What fraction of your budget do you spend on popcorn