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 =

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Chapter1: Making Economics Decisions
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• 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?
Transcribed Image Text:• 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
=
Transcribed Image Text: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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