A glass manufacturer's production function is q=10*L^0.5*K^0.5(based on Hsieh, 1995). Its marginal product functions are MP_L=5K^0.5*L^0.5=0.5q/L and MP_K= (5L^0.5)/(K^0.5)=(0.5q)/K. Suppose that its wage, w, is $1 per hour and the rental cost of capital, r, is $4. Draw an accurate figure showing how the glass firm minimizes its cost of production.

a. What is the equation of the (long-run) expansion path for a glass firm? Illustrate this path in a graph.

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

c. Suppose the goal for output is 1000 units, what is the optimal level of labor and capital to minimize the cost of production? (Use Excel or other software to derive the answer.