Suppose a brewery uses a cobb-douglas production function

Question

Suppose a brewery uses a Cobb-Douglas production function for his production. He studies the production process and finds the following. An additional machine-hour of fermentation capacity would increase output by 400 bottles per day (i.e.MPK=400). An additional man-hour of labor would increase output by 900 bottles per day (i.e.MP

L=900). The price of a man-hour of labor is $18 per hour. The price of a machine-hour of fermentation capacity is $5 per hour.

1. Is the brewery currently minimizing its cost of production? Check using the minimization condition.
2. It turns out, the brewery is not optimally chossing the factors of production. To lower its production cost, which factor of production should the brewery increase and which factor should he decrease?
3. Suppose that the price of a machine-hour of fermentation capacity rises to $8 per hour. How does this change the answer from part 1?