2. (36 points) A rm produces a product 3; using the production technology 1/2 1/2 y = f ($1,332) = 23:1 332 , where :31 and 232 are the inputs used for the production. Suppose that the rm is using E2 = 9 units of input 2 and is unable to vary this quantity in the short-run. In the short-run, the only thing that is left for the rm to choose is the amount of input 1. Let the input prices be 1.01 = $6 and 1.02 = $2, and the output price be p = $2. 3.. b. Write the rm's short-run prot-maximization problem and nd the amount of input 931 used to maximize its short-run prot. Suppose that the price of input 2 changes to ma = $4. How does your answer to part (a) change? What if the new output price is p' = $4? How does your answer to part (a) change? . Keep the prices at wl = $6, 202 = $2, and p = $2. What is the minimum short-run cost of producing 12 units of output? . In the long-run, what are the inputs 3:1 and 2:2, and the long-run cost of producing 12 units of output? (round your answers to two decimal places)