Suppose a Cobb-Douglas Production function is given by the function: P(L, K) = 13L0.2 K0.8 Furthemore, the cost function for a facility is given by the function:C(L, K) = 400L + 500K
a
Suppose the monthly production goal of this facility is to produce 17,000 items. In this problem, we will
assume L represents units of labor invested and K 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 La
(Show your answer is exactly 1 decimal place)
Units of Capital K =
(Show your answer is exactly 1 decimal place)
Also, what is the minimal cost to produce 17,000 units? (Use your rounded values for L and K from above
to answer this question.)
The minimal cost to produce 17,000 units is $
Hint:
1. Your constraint equation involves the Cobb Douglas Production function, not the Cost function.
2. When finding a relationship between L and K in your system of equations, remember that you will
want to eliminated to get a relationship between L and K.
3. Round your values for L and K to one decimal place (tenths).