a)A cost minimizing firm's production is given by Q=L^(1/2)K^(1/2). Suppose the desired output is Q=10. Let w=12 and r=4. What is the firms cost minimizing combination of K and L? What is the total cost of producing output?
b) Suppose the firm wishes to increase its output to Q=12. In the short run, the firms K is fixed at the amount found in (a), but L is variable. How much labor will the firm use? What will the total cost be?