This is about consumer theory in microeconomics. Please show all your workings and explanations and answers. Please answer all parts

Question One (7 Marks) Ms Caffeine enjoys coee (C) and tea (T) according to the function U( T, C) = 41" + 3C. (a) What does her utility function say about her MRS of coffee for Tea? What do her indifference curves look like? (b) If coffee and tea cost $3 each, and MS. Caffeine has $12 to spend on these products, how much coffee and tea should she buy to maximise her utility? (c) Draw the graph of her indifference curve and budget constraint showing the utility- maximising point. ((1) How would her consumption change if the price of coffee fell to $2