(d) If a small change occur for the profit of Alpha machine; in what range of the change could remains the current optimal?
(d) If a small change occur for the profit of Alpha machine; in what range of the change could remains the current optimal?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 8T
Related questions
Question
100%
I need D pls
![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%2Ff5f852bf-2790-48ca-a221-2e4e6b0c5bab%2Fd3jnfh_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.
![(d) If a small change occur for the profit of Alpha machine; in what range of the change could
remains the current optimal?
(e) On the basis of (d), compute the objective coefficient range for Alpha machine so that the
current optimal remains unchanged.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdee279f8-9725-4f86-9612-6ea1f27d04ad%2Ff5f852bf-2790-48ca-a221-2e4e6b0c5bab%2Fkw454t_processed.png&w=3840&q=75)
Transcribed Image Text:(d) If a small change occur for the profit of Alpha machine; in what range of the change could
remains the current optimal?
(e) On the basis of (d), compute the objective coefficient range for Alpha machine so that the
current optimal remains unchanged.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 5 steps with 1 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![College Algebra](https://www.bartleby.com/isbn_cover_images/9781337282291/9781337282291_smallCoverImage.gif)
![Intermediate Algebra](https://www.bartleby.com/isbn_cover_images/9781285195728/9781285195728_smallCoverImage.gif)
Intermediate Algebra
Algebra
ISBN:
9781285195728
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![College Algebra](https://www.bartleby.com/isbn_cover_images/9781337282291/9781337282291_smallCoverImage.gif)
![Intermediate Algebra](https://www.bartleby.com/isbn_cover_images/9781285195728/9781285195728_smallCoverImage.gif)
Intermediate Algebra
Algebra
ISBN:
9781285195728
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
![Elementary Geometry For College Students, 7e](https://www.bartleby.com/isbn_cover_images/9781337614085/9781337614085_smallCoverImage.jpg)
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
![Intermediate Algebra](https://www.bartleby.com/isbn_cover_images/9780998625720/9780998625720_smallCoverImage.gif)
![Elementary Algebra](https://www.bartleby.com/isbn_cover_images/9780998625713/9780998625713_smallCoverImage.jpg)
Elementary Algebra
Algebra
ISBN:
9780998625713
Author:
Lynn Marecek, MaryAnne Anthony-Smith
Publisher:
OpenStax - Rice University