Maria is launching a start-up to make paper cups for

the coffee shops in the Boston area. To make cups,

she uses both labor (

L

) and equipment (capital, or

K

). Her production function is

4

.

.

, where

Q

is the number of cups produced, measured in thousa

nds. Labor and capital are Maria's only costs. The

daily wage (

w

) is $400 per person-day and the rental price of capital (

r

) is $100 per machine-day.

1. To get her start-up going, Maria initially hires 4 workers and rents 4 machines per day to produce 16

thousand cups per day.

a. Show that Maria is not minimizing her cost at this level of output.

b. What mix of inputs

L

and

K

could Maria use to make the same qu

antity of cups at a minimal cost?

c. How much would Maria save with th

e cost-minimizing choices of inputs?