ulia runs a coffee cart in the JSOM. It costs her $1 to produce each cup of coffee, and she observes a linear price-response function d(p) = (180 - 20p)+ for her coffee each day. a. Find the price per cup that maximizes Julia's net contribution, along with the resulting contribution. (10 points) b. Suppose large coffee chain proposes a deal to supply her with unlimited brewed coffee daily for a fixed cost of K dollars per day. If Julia agrees to this arrangement, what would be the optimal price per cup? (10 points) c. At what fixed cost K values would entering into this contract increase Julia's profits? (5 points) d. The chain now modifies the offer to a fixed daily cost of $50, but limits the supply to a maximum of 80 cups of coffee per day. Should Julia accept this revised proposal? Justify your