Computing the optimal level of inputs L* also K* which minimize the cost of producing.

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

1. Find the optimal level of inputs L* also K* which minimize the cost of producing Q0. Illustrate what is the cost of production associated to L* also K*?

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