Consider the following problem related to the output-maximizing manager. Production requires capital (K) and labour (L). The output level is given by the following function. Y(K,L)=L21K21 Capital costs r per unit, and labour costs w per unit. As a manager, you are told to produce an output of Y>0. Your problem is to choose K and L so as to produce this output at the lowest possible cost. Assume r=w=Y=1. a. Set up the problem, writing out the objective function, the constraint, and the Lagrangian function. b. Write the system of first-order conditions. Is this a linear system? c. Find the optimal values d. Verify the second-order condition is satisfied. e. Interpret the value of . Note: round your answers to 2 decimal places