A Japanese synthetic rubber manufacturer’s production function is q = 10L0.5K0.5 (Flath, 2011). Suppose that its wage, w, is $1 per hour and the rental cost of capital, r, is $4. 

a. Draw an accurate figure showing how the synthetic rubber manufacturer minimizes its cost of production.
b. What is the equation of the (long-run) expansion path for the manufacturer? Illustrate it in a graph. 

c. Derive the long-run total cost curve equation as a function of q.