Programming辅导、讲解R编程语言、辅导R程序
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Overview and Rationale
This assignment is designed to provide the students with hands-on experiences utilizing R
/ excel to optimize profits or costs via linear programming models in real-life applications.
You are provided with a business scenario and you are asked to create a model to optimize
profits and costs.
Course Outcomes
This assignment is directly linked to the following key learning outcomes from the course
syllabus:
CO1: Use descriptive, Heuristic and prescriptive analysis to drive business strategies
and actions
CO4: Incorporate general industry practices in end-to-end analytics development
cycles, including data management, data engineering, analytics modeling, optimization,
and strategic development
Assignment Summary
A Profit and Cost Model
A northern hardware company is studying a plan to open a new distribution center in
southeast. The company plans to rent a warehouse and an adjacent office, and distribute its
main products to the local dealers. The company has decided to initially start with four of
its main products: Pressure washers, Go karts, Generators, and Water pumps. The table
below describes how much each of the products will cost the company (including
transportation costs):
Item Cost (in Dollars)
Pressure Washer 330
Go-kart 370
Generator 410
Case of 5 Water Pumps 135
The company has set aside a purchasing monthly budget of $170,000 for the new location.
The selling prices (per unit) for each item are given in the table below:
Item Cost (in Dollars)
Pressure Washer 499.99
Go-kart 729.99
Generator 699.99
Case of 5 Water Pumps 269.99
Other than the budget, another of the company’s concern is the available space in the
warehouse. The warehouse has 82 shelves and each shelf is 30 ft long and 5 ft wide.
Pressure washers and generators each are stored on 5 ft by 5 ft pallets whereas each Go
Kart is stored on an 8 ft by 5 ft pallet. Furthermore, a 5 ft by 5 ft pallet is used to store five
cases of water pumps
For promoting its brand products, the company’s marketing department has decided to
allocate at least 30% of its inventory to pressure washers and Go Karts, and sell at least
twice as many generators as water pumps.
As a consultant, your task is perform a monthly analysis using a linear programming model
to maximize the company's net profit. Complete the following in a Word document and in
R. Submit both the Word document and the R/Excel file as attachments
1. In a Word document, write the mathematical formulation of the problem.
2. Set up the linear programming formulation in R/excel.
3. Use the LpsolveAPI/lpsolve in R/excel to solve the problem, and generate a report.
4. Describe the optimal solutions obtained in the Word document. These will consist of
the inventory level for all four products and the optimal monthly profit.
5. One of the decision variables has an optimal value of zero. Use the R report to
determine the smallest selling price for that item so that this optimal zero solution
value changes to a non-zero value.
6. In the word document explain whether, in addition to the $170,000 allocated to the
purchasing budget during the first month, the company should allocate additional
money. If yes, calculate the amount of additional investment do you recommend,
and how much should the company expect its net monthly profit to increase as a
consequence of this increase?
7. In the word document, explain whether you recommend that the company should
rent a smaller or a larger warehouse. In any case, indicate the ideal size of your
recommended warehouse in square feet, and indicate how much this change in the
size of the warehouse will contribute to the monthly profit.
Format & Guidelines
Submissions should consist of an R file/excel and a Word document. The report should
follow the following format:
(i) Introduction
(ii) Analysis
(iii) Conclusion
And be 1000 - 1200 words in length, not including the title page, and presented in the APA
format.
Rubric
Category Exceeds Standard Meets Standards Approaching
Standards Below Standards
R: Problem
Modeling &
Set-up
ALY6050-CO1
Completely and
concisely modeled
the problem in R for
each method
Accurately modeled
the problem in Excel
(or R) for each
method
Correctly modeled
the problem in Excel
(or R) for each
method, but the
model lacks detailed
insight into the
problem or the setup
is awkward.
Modeled the problem
in Excel (or R) for
each method, but
there are some gaps
in the problem
modeling and setup
R: Problem
Solution &
Accuracy
ALY6050-CO1
ALY6050-CO4
Efficiently obtained
correct and accurate
solutions in Excel (or
R) by using the
appropriate analytic
tools of the software
Obtained complete
and accurate
solutions in Excel (or
R) by using the
appropriate analytic
tools of the software
Obtained correct
solutions in Excel (or
R) using the
appropriate analytic
tools of the software,
but the application of
the tool is awkward.
Obtained a solutions
in Excel (or R) by
using the appropriate
analytic tools of the
software, but the
solution is not
complete.
Word/Report:
Problem
Description &
Introduction
ALY6050-CO4
Provides a thorough
and concise summary
of the problem
descriptions and
introduced the
problem using rich
and significant ideas
Provides an accurate
and succinct
summary of the
problem descriptions
and problem
introduction
Provides an accurate
summary of the
problem descriptions
and problem
introduction, but the
description is too
wordy or not
succinct
Provided a summary
of the problem
descriptions and
problem
introduction, but it is
inaccurate or
incomplete
Word/Report:
Description of
Problem
Analysis
ALY6050-CO4
Provides a thorough
and precise
description of the
analytic concepts and
theories used in
analyzing the
problem
Accurately describes
the analytic concepts
and theories used in
analyzing the
problem
Describes the
analytic concepts and
theories used in
analyzing the
problem, but
description lacks
appropriate detail or
precision
Describes the
analytical concepts
and theories used in
analyzing the
problem, but
descriptions are
incorrect or the
analytical concepts
and theories are
incorrect
Word/Report:
Description of
Conclusions
ALY6050-CO4
Provides conclusions
and results obtained
in the project using a
high level of critical
thinking and
reasoning
Provides relevant
conclusions and
results obtained in
the project that
reflect critical
thinking and
reasoning
Provides conclusions
and results obtained
in the project, but not
all conclusions or
results are relevant
to the problem or not
Provides conclusions
and results obtained
in the project, but
they are irrelevant
and reflect a lack of
critical thinking
Category Exceeds Standard Meets Standards
Approaching
Standards Below Standards
all conclusions reflect
good reasoning
Word/Report:
Writing
Mechanics,
Title Page, &
References
Completely free of
errors in grammar,
spelling, and
punctuation; and
completely correct
usage of title page,
citations, and
references. The
report contains a
minimum of 1000
words
There are no
noticeable errors in
grammar, spelling,
and punctuation; and
completely correct
usage of title page,
citations, and
references. The
report contains a
minimum of 1000
words
There are very few
errors in grammar,
spelling, and
punctuation; and
completely correct
usage of title page,
citations, and
references. The
report contains a
minimum of 1000
words
There are more than
five errors in
grammar, spelling,
and punctuation; or
the usage of title
page, citations, and
references are
incomplete; or the
report contains less
than 1000 words
Overview and Rationale
This assignment is designed to provide the students with hands-on experiences utilizing R
/ excel to optimize profits or costs via linear programming models in real-life applications.
You are provided with a business scenario and you are asked to create a model to optimize
profits and costs.
Course Outcomes
This assignment is directly linked to the following key learning outcomes from the course
syllabus:
CO1: Use descriptive, Heuristic and prescriptive analysis to drive business strategies
and actions
CO4: Incorporate general industry practices in end-to-end analytics development
cycles, including data management, data engineering, analytics modeling, optimization,
and strategic development
Assignment Summary
A Profit and Cost Model
A northern hardware company is studying a plan to open a new distribution center in
southeast. The company plans to rent a warehouse and an adjacent office, and distribute its
main products to the local dealers. The company has decided to initially start with four of
its main products: Pressure washers, Go karts, Generators, and Water pumps. The table
below describes how much each of the products will cost the company (including
transportation costs):
Item Cost (in Dollars)
Pressure Washer 330
Go-kart 370
Generator 410
Case of 5 Water Pumps 135
The company has set aside a purchasing monthly budget of $170,000 for the new location.
The selling prices (per unit) for each item are given in the table below:
Item Cost (in Dollars)
Pressure Washer 499.99
Go-kart 729.99
Generator 699.99
Case of 5 Water Pumps 269.99
Other than the budget, another of the company’s concern is the available space in the
warehouse. The warehouse has 82 shelves and each shelf is 30 ft long and 5 ft wide.
Pressure washers and generators each are stored on 5 ft by 5 ft pallets whereas each Go
Kart is stored on an 8 ft by 5 ft pallet. Furthermore, a 5 ft by 5 ft pallet is used to store five
cases of water pumps
For promoting its brand products, the company’s marketing department has decided to
allocate at least 30% of its inventory to pressure washers and Go Karts, and sell at least
twice as many generators as water pumps.
As a consultant, your task is perform a monthly analysis using a linear programming model
to maximize the company's net profit. Complete the following in a Word document and in
R. Submit both the Word document and the R/Excel file as attachments
1. In a Word document, write the mathematical formulation of the problem.
2. Set up the linear programming formulation in R/excel.
3. Use the LpsolveAPI/lpsolve in R/excel to solve the problem, and generate a report.
4. Describe the optimal solutions obtained in the Word document. These will consist of
the inventory level for all four products and the optimal monthly profit.
5. One of the decision variables has an optimal value of zero. Use the R report to
determine the smallest selling price for that item so that this optimal zero solution
value changes to a non-zero value.
6. In the word document explain whether, in addition to the $170,000 allocated to the
purchasing budget during the first month, the company should allocate additional
money. If yes, calculate the amount of additional investment do you recommend,
and how much should the company expect its net monthly profit to increase as a
consequence of this increase?
7. In the word document, explain whether you recommend that the company should
rent a smaller or a larger warehouse. In any case, indicate the ideal size of your
recommended warehouse in square feet, and indicate how much this change in the
size of the warehouse will contribute to the monthly profit.
Format & Guidelines
Submissions should consist of an R file/excel and a Word document. The report should
follow the following format:
(i) Introduction
(ii) Analysis
(iii) Conclusion
And be 1000 - 1200 words in length, not including the title page, and presented in the APA
format.
Rubric
Category Exceeds Standard Meets Standards Approaching
Standards Below Standards
R: Problem
Modeling &
Set-up
ALY6050-CO1
Completely and
concisely modeled
the problem in R for
each method
Accurately modeled
the problem in Excel
(or R) for each
method
Correctly modeled
the problem in Excel
(or R) for each
method, but the
model lacks detailed
insight into the
problem or the setup
is awkward.
Modeled the problem
in Excel (or R) for
each method, but
there are some gaps
in the problem
modeling and setup
R: Problem
Solution &
Accuracy
ALY6050-CO1
ALY6050-CO4
Efficiently obtained
correct and accurate
solutions in Excel (or
R) by using the
appropriate analytic
tools of the software
Obtained complete
and accurate
solutions in Excel (or
R) by using the
appropriate analytic
tools of the software
Obtained correct
solutions in Excel (or
R) using the
appropriate analytic
tools of the software,
but the application of
the tool is awkward.
Obtained a solutions
in Excel (or R) by
using the appropriate
analytic tools of the
software, but the
solution is not
complete.
Word/Report:
Problem
Description &
Introduction
ALY6050-CO4
Provides a thorough
and concise summary
of the problem
descriptions and
introduced the
problem using rich
and significant ideas
Provides an accurate
and succinct
summary of the
problem descriptions
and problem
introduction
Provides an accurate
summary of the
problem descriptions
and problem
introduction, but the
description is too
wordy or not
succinct
Provided a summary
of the problem
descriptions and
problem
introduction, but it is
inaccurate or
incomplete
Word/Report:
Description of
Problem
Analysis
ALY6050-CO4
Provides a thorough
and precise
description of the
analytic concepts and
theories used in
analyzing the
problem
Accurately describes
the analytic concepts
and theories used in
analyzing the
problem
Describes the
analytic concepts and
theories used in
analyzing the
problem, but
description lacks
appropriate detail or
precision
Describes the
analytical concepts
and theories used in
analyzing the
problem, but
descriptions are
incorrect or the
analytical concepts
and theories are
incorrect
Word/Report:
Description of
Conclusions
ALY6050-CO4
Provides conclusions
and results obtained
in the project using a
high level of critical
thinking and
reasoning
Provides relevant
conclusions and
results obtained in
the project that
reflect critical
thinking and
reasoning
Provides conclusions
and results obtained
in the project, but not
all conclusions or
results are relevant
to the problem or not
Provides conclusions
and results obtained
in the project, but
they are irrelevant
and reflect a lack of
critical thinking
Category Exceeds Standard Meets Standards
Approaching
Standards Below Standards
all conclusions reflect
good reasoning
Word/Report:
Writing
Mechanics,
Title Page, &
References
Completely free of
errors in grammar,
spelling, and
punctuation; and
completely correct
usage of title page,
citations, and
references. The
report contains a
minimum of 1000
words
There are no
noticeable errors in
grammar, spelling,
and punctuation; and
completely correct
usage of title page,
citations, and
references. The
report contains a
minimum of 1000
words
There are very few
errors in grammar,
spelling, and
punctuation; and
completely correct
usage of title page,
citations, and
references. The
report contains a
minimum of 1000
words
There are more than
five errors in
grammar, spelling,
and punctuation; or
the usage of title
page, citations, and
references are
incomplete; or the
report contains less
than 1000 words