Please help solve the attached question with steps. Thank you~

2. [20 POINTS] You run a cost-minimizing rm with production function y = f(L,K) = [miIl {3K 2113]\"3 where L is labor and K is capital. Assume that you pay to for each unit of labor you hire, 1* for each unit of capital, and face no costs other than those from labor and capital. Assume that the price of the output is given by p = yl/z. (a) [10 POINTS] Assuming that your rm is in long run problem, derive expressions for your costminimizing conditional input demands,L(r,w, y) and K (ryw, y) (b) [10 POINTS] Write down an expression for your total cost function C(r,w, y) and your prot function. Under which condition does the rm stay in the business