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BUAD 703-Week 6 Homework Assignment A start-up woodworking Week 6 Homework AssignmentA start-up woodworking company will be manufacturing and selling dining room tablesand chairs. The owner assumes that his prospective customers are interested in buyingta

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BUAD 703-Week 6 Homework Assignment A start-up woodworking

Week 6 Homework AssignmentA start-up woodworking company will be manufacturing and selling dining room tablesand chairs. The owner assumes that his prospective customers are interested in buyingtables and chairs individually rather than having to buy them in pre-defined sets, as is thecase with most furniture manufacturers. The following considerations apply to thecompany’s first month of production:The company’s objective is to maximize profit during each monthly productioncycle.The company will earn a potential profit of $300 for each table sold and $55 foreach chair sold.All tables and chairs manufactured during a given production period will be soldduring the same production period.Fabrication of each table requires 8 units of wood and each chair requires 2.5 unitof wood.Fabrication of each table requires 25 units of fabrication labor and each chairrequires 12 units of fabrication labor.Fabrication of each table requires 8 units of assembly labor and each chairrequires 5 units of assembly labor.Fabrication of each table requires 10.5 units of finishing labor and each chairrequires 8 units of finishing labor.Fabrication of each table requires 3 unit of packaging labor and each chairrequires 1.5 unit of packaging labor.Producing partially manufactured (i.e., partially fabricated, assembled, finishedand/or packaged) tables and/or chairs is acceptable during any given productionperiod since they can be completed during the subsequent production cycle.For the first month of production, the owner anticipates having 1,000 units ofwood, 3,000 units of fabrication labor, 2,000 units of assembly labor, 2,000 unitsof finishing labor and 500 units of packaging labor available.1. The company’s president has asked you to develop a linear programming modelusing the Excel Solver method in order to answer the following questions as part ofthe planning for the first month of production:a. What is the optimal number of tables the company should produce during theupcoming production cycle?b. What is the optimal number of chairs the company should produce during theupcoming production cycle?c. What is the total amount of profit that the company would earn for producingthe optimal number of complete tables and chairs during the upcomingproduction cycle (partially manufactured tables and/or chairs do not contributeto profit earned since they cannot be sold during the upcoming productioncycle)?d. Which resources will be fully used in producing the optimal number of tablesand chairs during the upcoming production cycle?1 of 32. After reviewing your recommendations based upon your original model, the presidenthas asked you to revise your original model to include the following additionalcriteria: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 ofthe revised planning for the first month of production:a. What is the optimal number of tables the company should produce during theupcoming production cycle?b. What is the optimal number of chairs the company should produce during theupcoming production cycle?c. What is the total amount of profit that the company would earn for producingthe optimal number of complete tables and chairs during the upcomingproduction cycle (partially manufactured tables and/or chairs do not contributeto profit earned since they cannot be sold during the upcoming productioncycle)?d. Which resources will be fully used in producing the optimal number of tablesand chairs during the upcoming production cycle?3. While the owner of the company was satisfied with your revised model, he decided tosurvey prospective customers prior to commencing production and discovered thatthe vast majority of his prospective customers are only interested in purchasing tableand chair sets, with each set consisting of one table and four chairs. Consequently, hehas requested that you revise your model to delete the requirement to produce aminimum of 50 tables and a minimum of 100 chairs, and instead include arequirement that exactly four chairs be produced for every table produced. Use yourrevised model and Excel Solver to answer the following questions as part of thefurther revised planning for the first month of production:a. What is the optimal number of tables the company should produce during theupcoming production cycle?b. What is the optimal number of chairs the company should produce during theupcoming production cycle?c. What is the total amount of profit that the company would earn for producingthe optimal number of complete tables and chair sets during the upcomingproduction cycle (i.e., partially manufactured tables and chairs, as well aspartial table and chair sets do not contribute to profit earned since they cannotbe sold during the upcoming production cycle)?d. Which resources will be fully used in producing the optimal number of tablesand chairs during the upcoming production cycle?4. During the first week of the initial production cycle a large number of the company’semployees have been stricken with the flu. The owner of the company has estimatedthat he will now only have 2,000 units of fabrication labor, 1,500 units of assemblylabor, 1,500 units of finishing labor and 300 units of packaging labor available for thefirst month of production. Revise your model from problem 3 to reflect the revised2 of 3resource quantities Use your revised model and Excel Solver to answer the followingquestions 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 theupcoming production cycle?b. What is the optimal number of chairs the company should produce during theupcoming production cycle?c. What is the total amount of profit that the company would earn for producingthe optimal number of complete tables and chair sets during the upcomingproduction cycle (i.e., partially manufactured tables and chairs, and/or partialtable and chair sets do not contribute to profit earned since they cannot be soldduring the upcoming production cycle)?d. Which resources will be fully used in producing the optimal number of tablesand 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., youcannot produce a negative number of tables or chairs).A given resource is fully consumed only if all of the resource has beenused (i.e., if even a fraction of the resource remains unused, then theresource has not been fully consumed).You do not need to create a separate variable to represent a table and chairset for problem 3 and 4. Instead, create a simple algebraic equation usingonly the two variables that represent the number of tables to be producedand the number of chairs to be produced that describes the exact ratio inwhich tables and chairs must be manufactured to produce complete sets.Do not forget to account for the constraint requiring that you produce a specificminimum number of table and chair sets in problems 3 and 4.Do not overlook the stipulation that only complete tables and/or chairs contributeto earned profit in problems 1 and 2.Do not overlook the stipulations that only complete table and chairs setscontribute to earned profit in problems 3 and 4.3 of 3

Week 6 Homework AssignmentA start-up woodworking company will be manufacturing and selling dining room tablesand chairs. The owner assumes that his prospective customers are interested in buyingtables and chairs individually rather than having to buy them in pre-defined sets, as is thecase with most furniture manufacturers. The following considerations apply to thecompany’s first month of production:The company’s objective is to maximize profit during each monthly productioncycle.The company will earn a potential profit of $300 for each table sold and $55 foreach chair sold.All tables and chairs manufactured during a given production period will be soldduring the same production period.Fabrication of each table requires 8 units of wood and each chair requires 2.5 unitof wood.Fabrication of each table requires 25 units of fabrication labor and each chairrequires 12 units of fabrication labor.Fabrication of each table requires 8 units of assembly labor and each chairrequires 5 units of assembly labor.Fabrication of each table requires 10.5 units of finishing labor and each chairrequires 8 units of finishing labor.Fabrication of each table requires 3 unit of packaging labor and each chairrequires 1.5 unit of packaging labor.Producing partially manufactured (i.e., partially fabricated, assembled, finishedand/or packaged) tables and/or chairs is acceptable during any given productionperiod since they can be completed during the subsequent production cycle.For the first month of production, the owner anticipates having 1,000 units ofwood, 3,000 units of fabrication labor, 2,000 units of assembly labor, 2,000 unitsof finishing labor and 500 units of packaging labor available.1. The company’s president has asked you to develop a linear programming modelusing the Excel Solver method in order to answer the following questions as part ofthe planning for the first month of production:a. What is the optimal number of tables the company should produce during theupcoming production cycle?b. What is the optimal number of chairs the company should produce during theupcoming production cycle?c. What is the total amount of profit that the company would earn for producingthe optimal number of complete tables and chairs during the upcomingproduction cycle (partially manufactured tables and/or chairs do not contributeto profit earned since they cannot be sold during the upcoming productioncycle)?d. Which resources will be fully used in producing the optimal number of tablesand chairs during the upcoming production cycle?1 of 32. After reviewing your recommendations based upon your original model, the presidenthas asked you to revise your original model to include the following additionalcriteria: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 ofthe revised planning for the first month of production:a. What is the optimal number of tables the company should produce during theupcoming production cycle?b. What is the optimal number of chairs the company should produce during theupcoming production cycle?c. What is the total amount of profit that the company would earn for producingthe optimal number of complete tables and chairs during the upcomingproduction cycle (partially manufactured tables and/or chairs do not contributeto profit earned since they cannot be sold during the upcoming productioncycle)?d. Which resources will be fully used in producing the optimal number of tablesand chairs during the upcoming production cycle?3. While the owner of the company was satisfied with your revised model, he decided tosurvey prospective customers prior to commencing production and discovered thatthe vast majority of his prospective customers are only interested in purchasing tableand chair sets, with each set consisting of one table and four chairs. Consequently, hehas requested that you revise your model to delete the requirement to produce aminimum of 50 tables and a minimum of 100 chairs, and instead include arequirement that exactly four chairs be produced for every table produced. Use yourrevised model and Excel Solver to answer the following questions as part of thefurther revised planning for the first month of production:a. What is the optimal number of tables the company should produce during theupcoming production cycle?b. What is the optimal number of chairs the company should produce during theupcoming production cycle?c. What is the total amount of profit that the company would earn for producingthe optimal number of complete tables and chair sets during the upcomingproduction cycle (i.e., partially manufactured tables and chairs, as well aspartial table and chair sets do not contribute to profit earned since they cannotbe sold during the upcoming production cycle)?d. Which resources will be fully used in producing the optimal number of tablesand chairs during the upcoming production cycle?4. During the first week of the initial production cycle a large number of the company’semployees have been stricken with the flu. The owner of the company has estimatedthat he will now only have 2,000 units of fabrication labor, 1,500 units of assemblylabor, 1,500 units of finishing labor and 300 units of packaging labor available for thefirst month of production. Revise your model from problem 3 to reflect the revised2 of 3resource quantities Use your revised model and Excel Solver to answer the followingquestions 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 theupcoming production cycle?b. What is the optimal number of chairs the company should produce during theupcoming production cycle?c. What is the total amount of profit that the company would earn for producingthe optimal number of complete tables and chair sets during the upcomingproduction cycle (i.e., partially manufactured tables and chairs, and/or partialtable and chair sets do not contribute to profit earned since they cannot be soldduring the upcoming production cycle)?d. Which resources will be fully used in producing the optimal number of tablesand 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., youcannot produce a negative number of tables or chairs).A given resource is fully consumed only if all of the resource has beenused (i.e., if even a fraction of the resource remains unused, then theresource has not been fully consumed).You do not need to create a separate variable to represent a table and chairset for problem 3 and 4. Instead, create a simple algebraic equation usingonly the two variables that represent the number of tables to be producedand the number of chairs to be produced that describes the exact ratio inwhich tables and chairs must be manufactured to produce complete sets.Do not forget to account for the constraint requiring that you produce a specificminimum number of table and chair sets in problems 3 and 4.Do not overlook the stipulation that only complete tables and/or chairs contributeto earned profit in problems 1 and 2.Do not overlook the stipulations that only complete table and chairs setscontribute to earned profit in problems 3 and 4.3 of 3



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