3) Consider a firm facing a wage rate of $6 and a rental rate of capital of $16. The company has allocated an outlay of $4.8 million for the initial production run. The production function using available technology can be expressed as:

Q = L0.5K0.25,

a. Determine the optimal input mix to get the maximum output for the initial outlay of $4.8m as well as that maximum output level.

b. Explain and illustrate what would happen in the short if output was increased by 25%. Would the capital labor combination change in the long run? If so, how would it change? How would the total cost compare in the short run and the long run?

c. Should the firm move to different location where w=4, r=20 assuming that relocation is costless?