3. A firm employs labor and capital by paying $40 per unit of labor (MCL) and $200 per hour to rent aunit of capital (MC). The production function is given by Q = 30L-2L2+ 120K-3K2, where Q istotal output.a.Derive MPL and MPKb.Determine the firm's optimal combination of capital (K) and labor (L)?Hint state the combination in the format L =Using your answer in part b, if the firm is committed to spending $3,240 on capital and laborper hour, how many units of labor (L) and capital (K) should the firm employ. Recall that the firmis paying $40 per unit of labor and $200 per hour to rent a unit of capital.d.How much output (Q) is produced if the firm uses the input values found in the previous question?

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3. A firm employs labor and capital by paying $40 per unit of labor (MCL) and $200 per hour to rent a unit of capital (MCK). The production function is given by Q=30L-2L2+ 120K -3K², where Q is total output. a. Derive MPL and MPK b. Determine the firm's optimal combination of capital (K) and labor (L)? Hint state the combination in the format L = C. Using your answer in part b, if the firm is committed to spending $3,240 on capital and labor per hour, how many units of labor (L) and capital (K) should the firm employ. Recall that the firm is paying per unit of labor and $200 per hour to rent a unit of capital. $40 d. How much output (Q) is produced if the firm uses the input values found in the previous question?