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##### The output (Q) of a production process is a function of two inputs (L and K) and is given by the following relationship:

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**Question**

The output (Q) of a production process is a function of two inputs (L and K) and;is given by the following relationship;Q = 0.50LK 0.10L2 0.05K2;The per-unit prices of inputs L and K are $20 and $25, respectively. The firm is;interested 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 them;equal to zero.;c. Solve the set of simultaneous equations in Part (b) for the optimal values of;L, K, and.;d. Based on your answers to Part (c), how many units of L and K should be;used by the firm? What is the total output of this combination?;e. Give an economic interpretation of the value determined in Part (c).

Paper#18310 | Written in 18-Jul-2015

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