Suppose a firm has the following production function: Q(L,K)=min{K,2L} Recall that the isocost line is as follows: C=wL+rK 1. What is the (long-run) optimal choice of Land K for a given Q,w, and r ? In other words, provide a formula for the optimal choice of labor L∗(w,r,Q) and capital K∗(w,r,Q) as a function of the parameters Q,w, and r. 2. Given Q=16,w=6, and r=2, what are the optimal levels of labor and capital, L∗ and K∗ ? What is the cost of producing Q=16 at these input prices? 3. Suppose now that you are in the short run, Q=16,w=6,r=2, and the capital level is fixed at Kˉ=20. What is the optimal level of labor in the short run? What is the cost of producing Q=16 in the short run at these input prices? Would it be possible to meet Q=16 if K=4 in the short run?