Week 6 Homework AssignmentA start-up woodworking company will be manufacturing and selling dining room tablesand chairs....
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Week 6 Homework Assignment
A start-up woodworking company will be manufacturing and selling dining room tables
and chairs. The owner assumes that his prospective customers are interested in buying
tables and chairs individually rather than having to buy them in pre-defined sets, as is the
case with most furniture manufacturers. The following considerations apply to the
companyâs first month of production:
The companyâs objective is to maximize profit during each monthly production
cycle.
The company will earn a potential profit of $300 for each table sold and $55 for
each chair sold.
All tables and chairs manufactured during a given production period will be sold
during the same production period.
Fabrication of each table requires 8 units of wood and each chair requires 2.5 unit
of wood.
Fabrication of each table requires 25 units of fabrication labor and each chair
requires 12 units of fabrication labor.
Fabrication of each table requires 8 units of assembly labor and each chair
requires 5 units of assembly labor.
Fabrication of each table requires 10.5 units of finishing labor and each chair
requires 8 units of finishing labor.
Fabrication of each table requires 3 unit of packaging labor and each chair
requires 1.5 unit of packaging labor.
Producing partially manufactured (i.e., partially fabricated, assembled, finished
and/or packaged) tables and/or chairs is acceptable during any given production
period since they can be completed during the subsequent production cycle.
For the first month of production, the owner anticipates having 1,000 units of
wood, 3,000 units of fabrication labor, 2,000 units of assembly labor, 2,000 units
of finishing labor and 500 units of packaging labor available.
1. The companyâs president has asked you to develop a linear programming model
using the Excel Solver method in order to answer the following questions as part of
the planning for the first month of production:
a. What is the optimal number of tables the company should produce during the
upcoming production cycle?
b. What is the optimal number of chairs the company should produce during the
upcoming production cycle?
c. What is the total amount of profit that the company would earn for producing
the optimal number of complete tables and chairs during the upcoming
production cycle (partially manufactured tables and/or chairs do not contribute
to profit earned since they cannot be sold during the upcoming production
cycle)?
d. Which resources will be fully used in producing the optimal number of tables
and chairs during the upcoming production cycle?
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2. After reviewing your recommendations based upon your original model, the president
has asked you to revise your original model to include the following additional
criteria:
A minimum of 50 tables shall be produced.
A minimum of 100 chairs shall be produced.
Use your revised model and Excel Solver to answer the following questions as part of
the revised planning for the first month of production:
a. What is the optimal number of tables the company should produce during the
upcoming production cycle?
b. What is the optimal number of chairs the company should produce during the
upcoming production cycle?
c. What is the total amount of profit that the company would earn for producing
the optimal number of complete tables and chairs during the upcoming
production cycle (partially manufactured tables and/or chairs do not contribute
to profit earned since they cannot be sold during the upcoming production
cycle)?
d. Which resources will be fully used in producing the optimal number of tables
and chairs during the upcoming production cycle?
3. While the owner of the company was satisfied with your revised model, he decided to
survey prospective customers prior to commencing production and discovered that
the vast majority of his prospective customers are only interested in purchasing table
and chair sets, with each set consisting of one table and four chairs. Consequently, he
has requested that you revise your model to delete the requirement to produce a
minimum of 50 tables and a minimum of 100 chairs, and instead include a
requirement that exactly four chairs be produced for every table produced. Use your
revised model and Excel Solver to answer the following questions as part of the
further revised planning for the first month of production:
a. What is the optimal number of tables the company should produce during the
upcoming production cycle?
b. What is the optimal number of chairs the company should produce during the
upcoming production cycle?
c. What is the total amount of profit that the company would earn for producing
the optimal number of complete tables and chair sets during the upcoming
production cycle (i.e., partially manufactured tables and chairs, as well as
partial table and chair sets do not contribute to profit earned since they cannot
be sold during the upcoming production cycle)?
d. Which resources will be fully used in producing the optimal number of tables
and chairs during the upcoming production cycle?
4. During the first week of the initial production cycle a large number of the companyâs
employees have been stricken with the flu. The owner of the company has estimated
that he will now only have 2,000 units of fabrication labor, 1,500 units of assembly
labor, 1,500 units of finishing labor and 300 units of packaging labor available for the
first month of production. Revise your model from problem 3 to reflect the revised
2 of 3
resource quantities Use your revised model and Excel Solver to answer the following
questions as part of the further revised planning for the first month of production:
a. What is the optimal number of tables the company should produce during the
upcoming production cycle?
b. What is the optimal number of chairs the company should produce during the
upcoming production cycle?
c. What is the total amount of profit that the company would earn for producing
the optimal number of complete tables and chair sets during the upcoming
production cycle (i.e., partially manufactured tables and chairs, and/or partial
table and chair sets do not contribute to profit earned since they cannot be sold
during the upcoming production cycle)?
d. Which resources will be fully used in producing the optimal number of tables
and chairs during the upcoming production cycle?
Hints for the preceding problems:
Do not forget to include a non-negativity constraint in your models (i.e., you
cannot produce a negative number of tables or chairs).
A given resource is fully consumed only if all of the resource has been
used (i.e., if even a fraction of the resource remains unused, then the
resource has not been fully consumed).
You do not need to create a separate variable to represent a table and chair
set for problem 3 and 4. Instead, create a simple algebraic equation using
only the two variables that represent the number of tables to be produced
and the number of chairs to be produced that describes the exact ratio in
which tables and chairs must be manufactured to produce complete sets.
Do not forget to account for the constraint requiring that you produce a specific
minimum number of table and chair sets in problems 3 and 4.
Do not overlook the stipulation that only complete tables and/or chairs contribute
to earned profit in problems 1 and 2.
Do not overlook the stipulations that only complete table and chairs sets
contribute to earned profit in problems 3 and 4.
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A start-up woodworking company will be manufacturing and selling dining room tables
and chairs. The owner assumes that his prospective customers are interested in buying
tables and chairs individually rather than having to buy them in pre-defined sets, as is the
case with most furniture manufacturers. The following considerations apply to the
companyâs first month of production:
The companyâs objective is to maximize profit during each monthly production
cycle.
The company will earn a potential profit of $300 for each table sold and $55 for
each chair sold.
All tables and chairs manufactured during a given production period will be sold
during the same production period.
Fabrication of each table requires 8 units of wood and each chair requires 2.5 unit
of wood.
Fabrication of each table requires 25 units of fabrication labor and each chair
requires 12 units of fabrication labor.
Fabrication of each table requires 8 units of assembly labor and each chair
requires 5 units of assembly labor.
Fabrication of each table requires 10.5 units of finishing labor and each chair
requires 8 units of finishing labor.
Fabrication of each table requires 3 unit of packaging labor and each chair
requires 1.5 unit of packaging labor.
Producing partially manufactured (i.e., partially fabricated, assembled, finished
and/or packaged) tables and/or chairs is acceptable during any given production
period since they can be completed during the subsequent production cycle.
For the first month of production, the owner anticipates having 1,000 units of
wood, 3,000 units of fabrication labor, 2,000 units of assembly labor, 2,000 units
of finishing labor and 500 units of packaging labor available.
1. The companyâs president has asked you to develop a linear programming model
using the Excel Solver method in order to answer the following questions as part of
the planning for the first month of production:
a. What is the optimal number of tables the company should produce during the
upcoming production cycle?
b. What is the optimal number of chairs the company should produce during the
upcoming production cycle?
c. What is the total amount of profit that the company would earn for producing
the optimal number of complete tables and chairs during the upcoming
production cycle (partially manufactured tables and/or chairs do not contribute
to profit earned since they cannot be sold during the upcoming production
cycle)?
d. Which resources will be fully used in producing the optimal number of tables
and chairs during the upcoming production cycle?
1 of 3
2. After reviewing your recommendations based upon your original model, the president
has asked you to revise your original model to include the following additional
criteria:
A minimum of 50 tables shall be produced.
A minimum of 100 chairs shall be produced.
Use your revised model and Excel Solver to answer the following questions as part of
the revised planning for the first month of production:
a. What is the optimal number of tables the company should produce during the
upcoming production cycle?
b. What is the optimal number of chairs the company should produce during the
upcoming production cycle?
c. What is the total amount of profit that the company would earn for producing
the optimal number of complete tables and chairs during the upcoming
production cycle (partially manufactured tables and/or chairs do not contribute
to profit earned since they cannot be sold during the upcoming production
cycle)?
d. Which resources will be fully used in producing the optimal number of tables
and chairs during the upcoming production cycle?
3. While the owner of the company was satisfied with your revised model, he decided to
survey prospective customers prior to commencing production and discovered that
the vast majority of his prospective customers are only interested in purchasing table
and chair sets, with each set consisting of one table and four chairs. Consequently, he
has requested that you revise your model to delete the requirement to produce a
minimum of 50 tables and a minimum of 100 chairs, and instead include a
requirement that exactly four chairs be produced for every table produced. Use your
revised model and Excel Solver to answer the following questions as part of the
further revised planning for the first month of production:
a. What is the optimal number of tables the company should produce during the
upcoming production cycle?
b. What is the optimal number of chairs the company should produce during the
upcoming production cycle?
c. What is the total amount of profit that the company would earn for producing
the optimal number of complete tables and chair sets during the upcoming
production cycle (i.e., partially manufactured tables and chairs, as well as
partial table and chair sets do not contribute to profit earned since they cannot
be sold during the upcoming production cycle)?
d. Which resources will be fully used in producing the optimal number of tables
and chairs during the upcoming production cycle?
4. During the first week of the initial production cycle a large number of the companyâs
employees have been stricken with the flu. The owner of the company has estimated
that he will now only have 2,000 units of fabrication labor, 1,500 units of assembly
labor, 1,500 units of finishing labor and 300 units of packaging labor available for the
first month of production. Revise your model from problem 3 to reflect the revised
2 of 3
resource quantities Use your revised model and Excel Solver to answer the following
questions as part of the further revised planning for the first month of production:
a. What is the optimal number of tables the company should produce during the
upcoming production cycle?
b. What is the optimal number of chairs the company should produce during the
upcoming production cycle?
c. What is the total amount of profit that the company would earn for producing
the optimal number of complete tables and chair sets during the upcoming
production cycle (i.e., partially manufactured tables and chairs, and/or partial
table and chair sets do not contribute to profit earned since they cannot be sold
during the upcoming production cycle)?
d. Which resources will be fully used in producing the optimal number of tables
and chairs during the upcoming production cycle?
Hints for the preceding problems:
Do not forget to include a non-negativity constraint in your models (i.e., you
cannot produce a negative number of tables or chairs).
A given resource is fully consumed only if all of the resource has been
used (i.e., if even a fraction of the resource remains unused, then the
resource has not been fully consumed).
You do not need to create a separate variable to represent a table and chair
set for problem 3 and 4. Instead, create a simple algebraic equation using
only the two variables that represent the number of tables to be produced
and the number of chairs to be produced that describes the exact ratio in
which tables and chairs must be manufactured to produce complete sets.
Do not forget to account for the constraint requiring that you produce a specific
minimum number of table and chair sets in problems 3 and 4.
Do not overlook the stipulation that only complete tables and/or chairs contribute
to earned profit in problems 1 and 2.
Do not overlook the stipulations that only complete table and chairs sets
contribute to earned profit in problems 3 and 4.
3 of 3
