A firm has three factories each producing the same item. Let x, y and z denote the respective output quantities that the three factories produce to fulfill an order of 2000 units in total. The cost functions for the three factories are the following: C₁(x) = 200 + C₂(y) = 200+ y + 1 100 1 -x² - y² + y 300 C3 (2) 200+ 10z =

A firm has three factories each producing the same item. Let x, y and z denote the respective output quantities that the three factories produce to fulfill an order of 2000 units in total. The cost functions for the three factories are the following: C₁(x) = 200 + C₂(y) = 200+ y + 1 100 1 -x² - y² + y 300 C3 (2) 200+ 10z =

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Concept explainers

Cost of Production

In economic theory, production costs are the costs incurred by an industrial organization when it engineers a project or provides a service that generates revenue and benefits. Labor costs, raw materials, consumable manufacturing costs, and general overhead sum up, accounting for production costs. Total cost data is calculated by combining total direct costs of materials, labor costs, and total production costs.

Question

• Find the values of x, y and z that minimize the total cost C.
• Verify that the solutions yield minimum costs.
• What is the minimum cost?

A firm has three factories each producing the same item. Let x, y and z denote the respective output
quantities that the three factories produce to fulfill an order of 2000 units in total. The cost functions for
the three factories are the following:
C₁(x) = 200 +
C₂(y) = 200 + y +
1
100
1
X
2
- y² + y
300
C3 (2) 200+ 10z
=

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