XP-Pen Corporation is one of the leading manufacturer of graphics tablets. The corporation has two types of machines to manufacture graphics tablets. Alpha machine has a production capacity of 25 graphics tablets per hour while Beta machine has a production capacity of 40 graphics tablets per hour. Both machines use the same raw material to produce graphics tablets yet at different rate of usage. Alpha machine uses 40 pounds of the raw material per hour while Beta machine uses 10 pounds more that Alpha machine per hour. Market predicts demand of the graphics tablets will increase in the upcoming week. Hence the retailers are willing to pay $18 for each graphics tablet XP-Pen Corporation can deliver. However, due to the downtime for maintenance, Alpha machine and Beta machine will be available for no more than 900 minutes and 600 minutes, respectively. Production manager of the corporation specified that the number of hours spent on Beta machine must be at least 40% of the number of hours spend on Alpha machine. Also, XP-Pen Corporation has a maximum of 1000 pounds of the raw material will be available for coming week's production; the cost of the raw material is $0.375 per ounce. XP- Pen Corporation estimated that the cost of operating the Alpha machine and Beta machine for every 30 minutes are $25 and $37.50, respectively. [1 pound = 16 ounces] (a) Formulate a linear programming model on deciding the number of hours that should be spent on the machines in order to maximize the profit contribution. (b) Find the feasible region by using graphical method and list all the extreme points. (c) What is the optimal number of hours that should be spent on the machines in order to maximize the profit contribution? State the maximum profit contributed.
XP-Pen Corporation is one of the leading manufacturer of graphics tablets. The corporation has two types of machines to manufacture graphics tablets. Alpha machine has a production capacity of 25 graphics tablets per hour while Beta machine has a production capacity of 40 graphics tablets per hour. Both machines use the same raw material to produce graphics tablets yet at different rate of usage. Alpha machine uses 40 pounds of the raw material per hour while Beta machine uses 10 pounds more that Alpha machine per hour. Market predicts demand of the graphics tablets will increase in the upcoming week. Hence the retailers are willing to pay $18 for each graphics tablet XP-Pen Corporation can deliver. However, due to the downtime for maintenance, Alpha machine and Beta machine will be available for no more than 900 minutes and 600 minutes, respectively. Production manager of the corporation specified that the number of hours spent on Beta machine must be at least 40% of the number of hours spend on Alpha machine. Also, XP-Pen Corporation has a maximum of 1000 pounds of the raw material will be available for coming week's production; the cost of the raw material is $0.375 per ounce. XP- Pen Corporation estimated that the cost of operating the Alpha machine and Beta machine for every 30 minutes are $25 and $37.50, respectively. [1 pound = 16 ounces] (a) Formulate a linear programming model on deciding the number of hours that should be spent on the machines in order to maximize the profit contribution. (b) Find the feasible region by using graphical method and list all the extreme points. (c) What is the optimal number of hours that should be spent on the machines in order to maximize the profit contribution? State the maximum profit contributed.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![XP-Pen Corporation is one of the leading manufacturer of graphics tablets. The corporation has
two types of machines to manufacture graphics tablets. Alpha machine has a production capacity
of 25 graphics tablets per hour while Beta machine has a production capacity of 40 graphics
tablets per hour. Both machines use the same raw material to produce graphics tablets yet at
different rate of usage. Alpha machine uses 40 pounds of the raw material per hour while Beta
machine uses 10 pounds more that Alpha machine per hour. Market predicts demand of the
graphics tablets will increase in the upcoming week. Hence the retailers are willing to pay $18
for each graphics tablet XP-Pen Corporation can deliver. However, due to the downtime for
maintenance, Alpha machine and Beta machine will be available for no more than 900 minutes
and 600 minutes, respectively. Production manager of the corporation specified that the number
of hours spent on Beta machine must be at least 40% of the number of hours spend on Alpha
machine. Also, XP-Pen Corporation has a maximum of 1000 pounds of the raw material will be
available for coming week's production; the cost of the raw material is $0.375 per ounce. XP-
Pen Corporation estimated that the cost of operating the Alpha machine and Beta machine for
every 30 minutes are $25 and $37.50, respectively.
[1 pound = 16 ounces]
(a) Formulate a linear programming model on deciding the number of hours that should be
spent on the machines in order to maximize the profit contribution.
(b) Find the feasible region by using graphical method and list all the extreme points.
(c) What is the optimal number of hours that should be spent on the machines in order to
maximize the profit contribution? State the maximum profit contributed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdee279f8-9725-4f86-9612-6ea1f27d04ad%2Fbf99a079-ea64-4873-894f-da74b7f13fba%2Fkletpm_processed.png&w=3840&q=75)
Transcribed Image Text:XP-Pen Corporation is one of the leading manufacturer of graphics tablets. The corporation has
two types of machines to manufacture graphics tablets. Alpha machine has a production capacity
of 25 graphics tablets per hour while Beta machine has a production capacity of 40 graphics
tablets per hour. Both machines use the same raw material to produce graphics tablets yet at
different rate of usage. Alpha machine uses 40 pounds of the raw material per hour while Beta
machine uses 10 pounds more that Alpha machine per hour. Market predicts demand of the
graphics tablets will increase in the upcoming week. Hence the retailers are willing to pay $18
for each graphics tablet XP-Pen Corporation can deliver. However, due to the downtime for
maintenance, Alpha machine and Beta machine will be available for no more than 900 minutes
and 600 minutes, respectively. Production manager of the corporation specified that the number
of hours spent on Beta machine must be at least 40% of the number of hours spend on Alpha
machine. Also, XP-Pen Corporation has a maximum of 1000 pounds of the raw material will be
available for coming week's production; the cost of the raw material is $0.375 per ounce. XP-
Pen Corporation estimated that the cost of operating the Alpha machine and Beta machine for
every 30 minutes are $25 and $37.50, respectively.
[1 pound = 16 ounces]
(a) Formulate a linear programming model on deciding the number of hours that should be
spent on the machines in order to maximize the profit contribution.
(b) Find the feasible region by using graphical method and list all the extreme points.
(c) What is the optimal number of hours that should be spent on the machines in order to
maximize the profit contribution? State the maximum profit contributed.
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