Consider a ski resort which uses capital K (mountains, ski lifts, lodges, etc.) and labor L (ski instructors, rental shop employees, kitchen staff, etc.) to accomodate q skiers per day according to the production function q = f(L, K) = (Krho + L rho ) 1 rho where 0 < rho ≤ 1. (1) Given the ski resort wants to accomodate q skiers at the minimum possible cost, solve for L ∗ (q) and K (q) in terms of wages w and the price of capital r.(2) Write down the problem the ski resort solves to find the levels of K and L that minimize cost. What two equations are used to solve it?(3) Suppose w = 1, r = 4, Find L*(q) and K*(q) for q = 500, q = 1000, and q = 2000. Plot these point on a graph and then sketch the expansion curve (4) For the same w = 1, r = 4, what is the ski resort's cost function C(q)? Graph it.