2. [25 points] Jim spends most of his time in Starbucks on Willis St. He has $12 per week to spend on coffee and muffins. Starbucks sells muffins for $2 each and coffee for $1.20 per cup. Jim consumes 7. cups of coffee and 9m muffins per week. Assume that he can buy fractions of these goods. His utility function is U(q. , 9m) = 92 9m". a. Draw Jim's budget line. b. Use the Lagrange technique to find Jim's optimal bundle. What utility does he attain? c. Now Starbucks has introduced a frequent buyer card. It costs $2 per week, but it gives him a discount of 20 cents per cup of coffee. If Jim buys this card, how will his consumption of coffee and muffins change? What utility will he attain? d. Should Jim buy this card