A rm has a production function _1.' = ththg} = hill\" + lll'g). Let the input prices be w] and \"'2, and the output price be p. (a) Write the rm's longnut prot-mindzation problem and solve for the factor demands .1"; and .13, the supply.r function 3"? and the maximized prots Jr'. (10 pts} (b) Show that the supply.r function has a positive slope. with respect to p. {5 p15} (c) Consider the short run case where E3. Now suppose that the price of 32 changes to a\": such that H": :v w: I: it increases}. Does this change the factor demand F2"? Does it change the supplyr function 3"? Does it change the maximized prots :1\"? In each case. explain brieyr Wh)r or whyr not. {11] pts]