2. [36 points} A rm produces 11 product y using the production technology y = 1" (r1, r2] = si'myz, where $1 and I; are the inputs used for the production. Suppose that the rmisusing Englmth-fiput Esndisunshletoysrythis qunntityinthe short run. In the shortrun, the only thing that is left for the rm to choose is the srnount of input 1. Let the input prices he to] = $ and 1112 = $2, and the output price be p = $2. .1. 1Write the rm's shortrun protInsatimisstion prohlmr and nd the amount of input 1:1 used to maximise its shortrun prot. [3 points] h. Suppose that the price of input 2 changes to is; = $4. How does your answer to pert {o} change? What if the new output price is p' = $4? How dog your answer to port (-11} change? [3 points} c. Kp the prica st wl = $ and to; = $2. 'W'hst is the minimum shortrun cost of producing 12 units of output?I [It] points} Id. In the longrun, what are the inputs $1 and $2, and the longrun cost of producing 12 units of output? (round your answers to two deciinsl places}. (10 points}