### Computing the optimal level of inputs

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A firm uses two inputs, unskilled labor (L) and capital (K) to produce its product. The wage rate for one unit of labor is \$5, while units of capital cost \$20. The firm's production function per day is Q (L, K) =4LK, while the MPL=4K and the MPK=4L. The firm wants to keep a constant production of Q0=400 units of output per day.

1. Find the optimal level of inputs L* and K* that minimize the cost of producing Q0. What is the cost of production associated to L* and K*?

In a graph depict the iso - quant for Q0 and the isocost associated to the solution in part a). Remember to put the intercepts and depict the optimal input levels L* and K*.

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