(2) A firm has two factories to produce widgets. Each factory has production function f(kr.4)=kil i=1,2. The factories differ, however, in the amount of capital equipment cach has. In particular, factory 1 has k = 25, whereas factory 2 has k=100. Price for capital and labor are r = $1 and w= $1. (a) If the firm wants to minimize short-run total cost of widget production, how should output be allocated between the two factories? (b) Given that output is allocated optimally between the two factories, calculate SC(q), SAC(q) and SMC(q). (e) Now suppose that firm can adjust ky and ky in the long-run. How should the firm allocate widget production between the two factories in the long-run? Calculate LC(q), LAC(q) and LMC(q). [HINT: Assume a division of total output q between the firms, say 91 and 92, and show that the cost does not depend on the division.]