3. (7 points) Prim has three hours a day to gather one of two plants: honeysuckle (), and pond lilies (/). Each honeysuckle takes 9 minutes to collect, and each pond lily takes 15 minutes to harvest. Further, suppose that Prim has a fixed amount of energy to use each day. She currently exhausts this entire energy by picking two honeysuckles and fifteen pond lilies. With this daily energy, she would also have been able to pick exactly seven honeysuckles and six pond lilies. Assume that both goods are perfectly divisible. a. Write down Prim's money and time constraints as algebraic inequalities. b. Show, using algebra, that Prim's two budget lines intersect at the bundle (h, [) = (5.5, 8.7). c. Plot Prim's energy constraint using a red dotted line. Plot Prim's time constraint using a blue dotted line. Clearly label each constraint, any axis intercepts, and any points of intersection between the two constraints. Shade in Prim's budget set, using solid black lines to indicate where the boundaries of the budget set are. 4. (13 points) Continue to consider Prim from Question 3. Suppose that Prim's preferences over honeysuckles and pond lilies are such that she likes them exactly equally: she is always willing to trade one honeysuckle for one pond liliy and remain exactly as well of as she was before. One valid utility representation of Prim's preferences is u(h,l) = h + [. a. On the same picture as before, plot indifference curves for the utility levels u = 5.8, 10, 14.2,18.4. b. Compute Prim's marginal utilities for each good. Using the marginal utility formulas you have just computed, prove that Prim's preferences are strongly monotone. C. 1. 1. ii. iii. Label three distinct bundles (h, ) on the indifference curve corresponding to a utility of 5.8. Hence, or otherwise, argue that his preferences are not strictly convex. i. Explain why Prim's optimal consumption bundle must lie on the outer boundary of her budget set. Identify Prim's optimal bundle by visual inspection. Briefly explain what you did. Find Prim's optimal consumption bundle using a mathematical argument