3. (20 points) Graph the budget constraints described in each of these situations Be sure to show your calculations! (a) (5 points) Suppose you are at a small chocolate shop. There are milk chocolate truffles (r) and dark chocolate truffles (y). You have $20 to spend and both truffles are $2 each. Graph the budget constraint on the graph below. (b) (5 points) A stressed out student trying to decide where to take yoga classes. They have $36 to spend on yoga classes this month. At SuperStrength yoga studio (I), the first 4 yoga classes are free. After that, SuperStrength yoga classes are $12 each. At the university gym (y), yoga classes come out to be about $3 per yoga class. Graph the budget constraint on the graph below.(c) (5 points) Let the price of a new magic lotion (x) be $4 per ounce for the first 81 = 4 ounces, and then $0.16 per ounce after that. The corresponding face wash (y) has a flat price of $1 per ounce. The consumer has $40 to spend on their new skincare regimen. Graph their budget constraint below. (d) (5 points) If the people in parts (a)-(c) all had rational, strictly convex and strongly monotone utility functions, such as u(x, y) = vay, do you expect there always to be a unique utility maximizing bundle for parts (a)-(c), respectively? Explain. (No calculation needed)