Suppose a Cobb-Douglas Production function is given by the function: P(L,K)=8L^0.7K^0.3 Furthemore, the cost function for a facility is given by the function:C(L,K)=300L+500K Suppose the monthly production goal of this facility is to produce 20,000 items. In this problem, we will assume LL represents units of labor invested and KK represents units of capital invested, and that you can invest in tenths of units for each of these. What allocation of labor and capital will minimize total production Costs? Units of Labor LL = (Show your answer is exactly 1 decimal place) Units of Capital KK = Incorrect (Show your answer is exactly 1 decimal place) Also, what is the minimal cost to produce 20,000 units? (Use your rounded values for LL and KK from above to answer this question.) The minimal cost to produce 20,000 units is $
Suppose a Cobb-Douglas Production function is given by the function: P(L,K)=8L^0.7K^0.3
Furthemore, the cost function for a facility is given by the function:C(L,K)=300L+500K
Suppose the monthly production goal of this facility is to produce 20,000 items. In this problem, we will assume LL represents units of labor invested and KK represents units of capital invested, and that you can invest in tenths of units for each of these. What allocation of labor and capital will minimize total production Costs?
Units of Labor LL = (Show your answer is exactly 1 decimal place)
Units of Capital KK = Incorrect (Show your answer is exactly 1 decimal place)
Also, what is the minimal cost to produce 20,000 units? (Use your rounded values for LL and KK from above to answer this question.)
The minimal cost to produce 20,000 units is $
Hint:
- Your constraint equation involves the Cobb Douglas Production function, not the Cost function.
- When finding a relationship between LL and KK in your system of equations, remember that you will want to eliminate λλ to get a relationship between LL and KK.
- Round your values for LL and KK to one decimal place (tenths).
Trending now
This is a popular solution!
Step by step
Solved in 7 steps
