You have the Cobb-Douglas utility function u(x,y) = xy over apples (x) and plums (y) and you have $120 budget to spend and can carry at most 480 ounces in weight in your backpack going back to the dorm. Each apple costs $1 and weighs 8 ounces, and each plum costs $3 and weighs 4 ounces. You can only leave the store with a bundle of fruits you can afford and carry.

(a) Drawing the relevant lines, intercepts, marking the points and hence identifying the feasible set of bundles, calculate the optimal bundle.

(b) Forget about (a). If you were to choose a backpack before going on this shopping trip, for the weight constraint not to be an issue for you, how many ounces of weight capacity would you need for your backpack? HINT: That is, for this weight capacity of the backpack, you'd be able to carry the best bundle you can afford, i.e, the weight constraint is not binding for your decision.

( c) Forget about (b). In (a), just before going out for shopping with your backpack to buy the bundle you have calculated in (a), you realize that you can take Uber (cars have no carrying capacity constraint, you can carry any weight of groceries you want). At most how much would you be willing to pay for Uber?