(25 points) Suppose that a consumer considers coffee and tea to be perfect substitutes, but he/she requires two cups of tea to give up three cups of coffee. This consumer's budget constraint can be written as 10C+T=10. Put coffee on the x-axis. a. (5 points) Write down a utility function that would best describe a consumer's preferences for tea and coffee. b. ( 5 points) How many cups of coffee and tea should the consumer buy to maximize the utility? c. (5 points) Graph the budget constraint, the optimal bundle, the indifference curve, and the utility level. Make sure you label everything. Put coffee on the x-axis. d. (5 points) Now, the price for coffee fell down to $0.5. Then, how many cups of coffee and tea should the consumer buy to maximize the utility? e. (5 points) Based on obtained optimal condition in part (c), graph the budget constraint, the optimal bundle, the indifference curve, and the utility level. Make sure you label everything. Put coffee on the x-axis