A company is refurbishing smartphones out of used smartphones. They are able to produce three different quality levels (Gold, Silver, and Bronze). The revenue for selling x, y, and z units of the respective devices can be calculated as R(x, y, z) = 600x + 400y + 300z – x2 – y? – 22. In order to refurbish the devices, they need to run through fine-tuned automated machines and have to pass a final quality check, which is done by employees. The required time for these two processes per quality level and the daily available machine and employee working times are displayed in the following table: machine minutes employee minutes Gold 60 Silver 40 Bronze 30 daily available time 800 100 The company wants to maximize the daily profit while using all available resources. Please calculate the critical points of that optimization problem. What is the respective revenue?

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter13: Regression And Forecasting Models
Section: Chapter Questions
Problem 31P
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A company is refurbishing smartphones out of used smartphones. They are able to produce three
different quality levels (Gold, Silver, and Bronze). The revenue for selling x, y, and z units of the
respective devices can be calculated as R(x, y, z) = 600x + 400y + 300z – x² – y? – 22. In order to
refurbish the devices, they need to run through fine-tuned automated machines and have to pass a
final quality check, which is done by employees. The required time for these two processes per quality
level and the daily available machine and employee working times are displayed in the following table:
machine minutes employee minutes
Gold
60
Silver
40
Bronze
30
daily available time
800
100
The company wants to maximize the daily profit while using all available resources. Please calculate
the critical points of that optimization problem. What is the respective revenue?
Transcribed Image Text:A company is refurbishing smartphones out of used smartphones. They are able to produce three different quality levels (Gold, Silver, and Bronze). The revenue for selling x, y, and z units of the respective devices can be calculated as R(x, y, z) = 600x + 400y + 300z – x² – y? – 22. In order to refurbish the devices, they need to run through fine-tuned automated machines and have to pass a final quality check, which is done by employees. The required time for these two processes per quality level and the daily available machine and employee working times are displayed in the following table: machine minutes employee minutes Gold 60 Silver 40 Bronze 30 daily available time 800 100 The company wants to maximize the daily profit while using all available resources. Please calculate the critical points of that optimization problem. What is the respective revenue?
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