Utility maximization in the case of perfect substitutes. Ms. Caffeine enjoys coffee (C) and tea (T) according to the function U(C, T) = 3C + 4T Prices of tea and coffee are each $3 and Ms. Caffeine has $12 to spend on these products. Please solve the question such that you plot C in the x-axis and T in the y-axis. a. What does her utility function say about her MRS of coffee and tea? What do her indifference curves look like? b. How much coffee and tea should she buy to maximize her utility? c. Draw the graph of her indifference curve map and her budget constraint, and show the utility-maximizing point. Please label all elements of the graph carefully d. Would this person buy any coffee if she had more money to spend? e. How would her consumption change if the price of coffee fell to $2