Question;The output (Q) of a production process is a function of two inputs (L and K) andis given by the following relationship:Q = 0.50LK 0.10L2 0.05K2The per-unit prices of inputs L and K are $20 and $25, respectively. The firm isinterested in maximizing output subject to a cost constraint of $500.a. Formulate the Lagrangian function:LQ = Q (CLL + CKK C)b. Take the partial derivatives of LQ with respect to L, K, and, and set themequal to zero.c. Solve the set of simultaneous equations in Part (b) for the optimal values ofL, K, and.d. Based on your answers to Part (c), how many units of L and K should beused by the firm? What is the total output of this combination?e. Give an economic interpretation of the value determined in Part (c).
Paper#56082 | Written in 18-Jul-2015Price : $22