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# Suppose a Cobb-Douglas Production function is given by the function: `P(L,K)=14 L^0.9 K^0.1*

Furthermore, the cost function for a facility is given by the function: `C(L,K)=400 L+100 K

Suppose the monthly production goal of this facility is to produce 18,000 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 L=

place)

Units of Capital K` =

place)

Also, what is the minimal cost to produce 18,000 units? (Use your rounded values for 'L' and 'K'

from above to answer this question.)

The minimal cost to produce 18,000 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 eliminate `lambda` to get a relationship between L and `K".

3. Round your values for Land "K" to one decimal place (tenths).