A fast-food company in Hermanus has the following cost function: TC = 10 + 3K + 2L, where Lis the number of labour hours and K is the number of machines they have to use. They have a production function of Q = 2KL, where Q represents the number of meals produced per day. The company has to make at least 75 meals every day. Using the Lagrangian method of production optimization, calculate the optimal number of labourers and machines needed to meet this quota. (6]

A fast-food company in Hermanus has the following cost function: TC = 10 + 3K + 2L, where Lis the number of labour hours and K is the number of machines they have to use. They have a production function of Q = 2KL, where Q represents the number of meals produced per day. The company has to make at least 75 meals every day. Using the Lagrangian method of production optimization, calculate the optimal number of labourers and machines needed to meet this quota. (6]

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

7. A fast-food company in Hermanus has the following cost function: TC = 10 + 3K +
2L, where L is the number of labour hours and K is the number of machines they
have to use. They have a production function of Q = 2KL, where Q represents the
number of meals produced per day. The company has to make at least 75 meals
every day. Using the Lagrangian method of production optimization, calculate the
optimal number of labourers and machines needed to meet this quota.
(6)

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