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Answer to Question #4506 in Microeconomics for Marcos

Question #4506
The Neo Corporation produces dream machines (software and hardware) that allows customers plugged in
to customize their dreams (e.g. you can be a pilot, or a martial arts expert). The Neo Corporation
production function is given by:
Q = 8L
0.5
K
0.5
,
where Q = output measured in number of dream machines,
L = labor measured in number of workers, and K = capital measured in number of mainframes. Neo
currently pays a wage of $400 per worker and considers the relevant rental price for capital to be $2500 per
mainframe.

Refer to Scenario 1. If Neo wants to produce 40 dream machines the optimal number of
workers to be hired is
a. Less than 2.
b. More than 2 but less than 4
c. More than 4 but less than 6
d. More than 6 but less than 8
e. More than 8
The answer is 8 but I don't know how.
Expert's answer
data:image/png;base64,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
The answer is e(more than 8) as L=12,5

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