A firm which produces 5000 tyres per day has the following production function:

Q=5K^(1/2) L^(1/2)

Where Q is the quantity of tyres produced, K is the number of hours for which the tyre making machine is used, and L is the number of person-hours required to produce tyres for a given day.

The company can currently use the equivalent of 200 hours of capital per day to produce 5000 tyres per day. The cost of the machine is of 250/hour, and employees are paid 20/hour.

In the long run, how much labour (in person-hours) and how much capital (in hours per day) should the company use to efficiently produce the same quantity of tyres per day? Illustrate on one graph the situation in the short run and in the long run. What will the average cost be? Compare your results with those obtained for question b) and explain.