Nike produces its sneakers using labor (L) and capital (K). Nike has the following production function Q = 50K1/5L1/4. The wage rate (PL) is $2 and the price of capital (PK) is $5. Nike wants to produce 1000 sneakers at the lowest possible cost.
(a) Use the Lagrangian Method to find the cost-minimizing quantity of capital and labor to produce 1000sneakers? Round your answers to two decimal places. Assume Nike uses fractional inputs.
(b) What is the total cost of producing 1000 sneakers?
(c) Calculate λ. What is the economic interpretation of this value?
(d) Suppose that the price of labor doubles to PL = $4. Assume all other variables are held constant.Find the new cost-minimizing quantity of capital and labor.