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Professors Ignacio and Felipe will teach the Introduction to Microeconomics classes at the university during the first semester of 2021.
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# Professors Ignacio and Felipe will teach the Introduction to Microeconomics

classes at the university during the first semester of 2021. And as economists they have decided to express the production function of the classes as follows:

q = i2/3 f1/3

Where
q = number of hours of classes taught
i = number of hours worked by Professor Ignacio
f = number of hours worked by Professor Felipe
Professor Ignacio values ​​his work at US \$ 80 per hour of work, and due to his experience in 2020, he already has his class material ready for which he dedicated 512 hours. Now Professor Felipe, whose work is valued at US \$ 20 an hour, must prepare the assistantships to complete all the classes for the semester.

a- How many hours will Felipe have to spend to produce a total of 150 hours of class? And if they decide to dictate 300 hours? And 100? (round to 1 decimal place)

b- What is the marginal cost of the 150 class hour? What about the 300 hour? And of the 100?

c- With the information from the statement, define the equilibrium condition that minimizes the cost of production, and find the optimal number of hours that Felipe should dedicate to the production of the classes, knowing that Professor Ignacio has already dedicated 512 hours.

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