2. Suppose Gi-hun produces dalgona (D) using two inputs: honey (H), and labor (L). Gi-hun's production function is D=H1/3L1/3. He sells dalgona in a competitive market at a price of 600 won. Honey costs 50 won per unit, and labor costs 100 won per unit. a. Write down the Gi-hun's profit function. b. Suppose in the short run, honey is fixed at H=18. Find the first order condition for the short-run profit-maximizing amount of labor. c. Solve for the amount of labor that Gi-hun uses in the short run to maximize profit. d. In the long run, both inputs are variable. Find the first order conditions for the long-run profit-maximizing amounts of both inputs. e. Solve for the amount of both inputs that maximize profit in the long run.