Suppose a profit-maximizing producer has the following production function: (k,l)=k ^1/2,l ^1/5 using input labor l and capital k

a).If the firm hires the same amount of labor and capital, what is the value of the MRTS? If w=10, r = 10, is the current input of labor and capital (i.e. using the same amount of labor and capital) cost- minimizing?

b). Suppose the firm initially has capital stock k=100, and is faced with capital rental cost r=1, wage w=1. Decide how much labor input the firm would employ to minimize its cost and the total production.

c). Now the firm wants to expand its production to 120 units in the short run when capital is fixed, how much labor and capital will the firm use? Is it cost-minimizing (r and w are the same as in (b))? What is the cost of producing these 120 units in the short run?

d).If the demand is strong that the firm now will expand its production to 120 units permanently. How much labor and capital will the firm use? Is it cost-minimizing? How does the labor and capital input in (d) compare to in (c)? What is the cost of producing the 120 units now?

e). Using one or more diagrams, qualitatively illustrate a firm's long- term vs short-term cost curves (average cost and marginal cost), and explain briefly why.

plz answer correct a to e explain

Dont answer by pen pepar