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Harrison Electronics Corporation Harrison Electronics Corporation (HEC) of Wayne, Indiana, is involved in selecting suppliers to be granted...

1. Harrison Electronics Corporation
Harrison Electronics Corporation (HEC) of Wayne, Indiana, is involved in selecting suppliers to be granted contracts to supply HEC with four different components to be used in a new product. Four suppliers have submitted bids on the components as shown in the table below with bid prices per unit for each component. Blank entries indicate that a supplier did not bid on a component.

Component
Supplier
1 2 3 4
Demand (units)

1 $20 $23 - $25 10,000
2 - $75 $70 $77 25,000
3 $25 $23 $28 - 5,000
4 $35 - - $37 15,000

HEC does not require sole-sourcing for its components, that is, more than one supplier can be the source of any particular component. This is critical, since some suppliers have limitations on their capacity to meet the demand for certain parts. Specifically:


• Supplier 1 is limited to a maximum of 15,000 units of component 4
• Supplier 2 is limited to a maximum of 2,500 units of component 1
• Supplier 4 is limited to a maximum of 12,000 units of component 2
• Supplier 4 is limited to a maximum of 3,500 units of component 4
In a letter submitted with its bid, supplier 4 indicated that it would have to contract for at least $460,000 in components from HEC or the bid would have to be withdrawn. Given such situations, HEC does not require that contracts be awarded strictly to the lowest bidders. In determining the contract awards, HEC has established the following goals, in order of priority:


• Total purchases must not exceed $3,000,000
• Provide supplier 4 with sufficient contract requirements that their bid is not withdrawn.
• Limit total contracts with any supplier to $980,000.
• Maintain the long-standing relationship with supplier 1 by providing it with a total contract amount of at least $900,000.
a. Formulate a linear programming model that can be used to determine the number of units of components, by type, contracted with each supplier to best achieve the goals of Harrison Electronics Corporation.
b. Determine the optimal contract plan using the Management Scientist software, including the quantity of each component from each supplier, the total cost of the contract plan developed, and the levels of goal achievement.
c. Provide a complete narrative that explains the Management Scientist solution used and the evidence of goal achievement or failure indicated.
2. Hathaway Manufacturing Company
Hathaway Manufacturing Company is developing the monthly production plan for three of its products: Product A, Product B, and Product C. The fabricating department can complete 10 units of Product A in 1 hour, or 15 units of Product B. A unit of Product C can be fabricated in 5 minutes. The department has 250 hours available for the month to be scheduled for these products with overtime available at an additional cost of $15 per hour. Each of the products requires time in the paint department with each unit of Product A needing 20 minutes, each unit of Product B needing 24 minutes, and each unit of Product C needing 30 minutes for the painting operation. There are 1,500 hours currently available in the paint department to be scheduled for these products. Overtime is not available in the paint department. The company has determined that it cannot sell more than 3,000 units of all of the products combined in the planning month. It has been the company's policy to produce at least 200 units of Product B each month.The products' unit contributions to profit are $20, $28, and $40 for products A, B, and C, respectively. The company's goals, in order of importance, are:
• A monthly profit contribution level for the combination of these products manufactured of at least $120,000.
• The use of overtime in the fabricating department in the month should be limited to a cost of not more than $1,000
• Hours scheduled in the paint department should not exceed 1,200.
• A minimum of at least 200 units of Product B should be produced.
a. Formulate a linear programming model that can be used to determine the optimal production schedule that will best achieve the company's goals.
b. Determine the optimal production schedule for Hathaway Manufacturing Company using the Management Scientist software, including the quantity of the products produced, the hours of production utilized, and the levels of goal achievement.
c. Provide a complete narrative that explains the Management Scientist solution used and the evidence of goal achievement or failure indicated.
3. ComPro Corporation
ComPro Corporation specializes in the assembly, sale, and installation of Dell, Inc. desktop computers to colleges and universities in the Southwestern United States. Compro ships the computers from three distribution centers located in Richmond, Virginia; Atlanta, Georgia; and Washington D.C. Four universities have ordered computers that must be delivered and installed before the end of the fall semester. The schools, Texas Tech; Texas A&M; Florida State; and North Carolina Central, require 520, 250, 400, and 380 units respectively, of the same model and installation configuration. The shipping and installation costs per computer from each of the distribution facilities to each school are given below:

Texas Tech
Texas A&M
Florida State
NC Central
Richmond $22 $17 $30 $18
Atlanta 15 35 20 25
Washington D. C. 28 21 16 14

ComPro has 420 units of the required model at its Richmond facility, 610 units at the Atlanta facility, and 340 units at the Washington facility. Given that demand for these units exceeds the available supply, ComPro has determined that it can satisfy slightly less than 90% of the demand from customers at an optimal total minimum transportation/installation cost of $22,470. To deflect some of the service concerns expected from customers, ComPro has elected to deviate from its original objective of cost minimization and has developed the following goals, arranged in the order of importance:
• Texas A&M is one of the longest term customers in the companys' history and ComPro wants the school to receive all of the units ordered.
• Recent negotiations with a trucking company union require that ComPro ship at least 80 units from the Washington D.C. facility to the campus of North Carolina Central.
• In order to maintain the best possible relations with all of its customers, ComPro wants to meet at least 80% of each schools' unit requirements.
• ComPro would like to keep any increase in the total costs of transportation and installation to no more than 10% of its original minimum calculation.
• Dissatisfaction with the trucking firm used to ship units from the Atlanta facility to Florida State has caused customer relations difficulties for ComPro and the number of units shipped over this route should be minimized,
a. Formulate a linear programming model that can be used to determine the number of units shipped from each distribution facility to each customer campus to best achieve the goals of ComPro Corporation.
b. Determine the optimal shipment plan using the Management Scientist software, including the quantity of each shipment from each distribution facility to each customer, the total number of units received by each customer, the total cost of the shipment plan developed, and the levels of goal achievement.
c. Provide a complete narrative that explains the Management Scientist solution used and the evidence of goal achievement or failure indicated.
4. Los Angeles City Council
The campaign manager for a candidate running for reelection to the Los Angeles City Council is developing a strategy for the initial months of the upcoming campaign. Four campaign media opportunities have been selected: TV spots, radio spots, billboards, and newspaper ads. Costs for each of these are $9,000 for each TV spot, $5,000 for each radio spot, $6,000 for a billboard ad for one month, and $1,800 for each newspaper ad. The audience reached by each type of media has been estimated to be 40,000 for each TV spot, 32,000 for each radio spot, 34,000 for each billboard ad for a month, and 17,000 for each newspaper ad. The total monthly campaign media budget is $160,000. The campaign manager has established the following goals for the first month, in order of priority:
• The audience reached should number at least 1,500,000.
• The total monthly campaign media budget should not be exceeded.
• The total of TV spots and radio spots, taken together, should be at least six.
• Not more than 10 campaign media ads of any one type should be used.
a. Formulate a linear programming model to determine the optimal mix that will best contribute to achievement of the campaign’s objective to maximize audience exposure for the candidate.
b. Determine the solution that would best achieve the campaign’s stated goals using the Management Scientist software, including the total audience reached, the number of each media type utilized, and the levels of goal achievement.
c. Provide a complete narrative that explains the Management Scientist solution used and the evidence of goal achievement or failure indicated..

1. Harrison Electronics Corporation Harrison Electronics Corporation (HEC) of Wayne, Indiana, is involved in selecting suppliers to be granted contracts to supply HEC with four different components to be used in a new product. Four suppliers have submitted bids on the components as shown in the table below with bid prices per unit for each component. Blank entries indicate that a supplier did not bid on a component. Compone nt Supplier 1 2 3 4 Demand (units) 1 $20 $23 - $25 10,000 2 - $75 $70 $77 25,000 3 $25 $23 $28 - 5,000 4 $35 - - $37 15,000 HEC does not require sole-sourcing for its components, that is, more than one supplier can be the source of any particular component. This is critical, since some suppliers have limitations on their capacity to meet the demand for certain parts. Specifically: Supplier 1 is limited to a maximum of 15,000 units of component 4 Supplier 2 is limited to a maximum of 2,500 units of component 1 Supplier 4 is limited to a maximum of 12,000 units of component 2 Supplier 4 is limited to a maximum of 3,500 units of component 4 In a letter submitted with its bid, supplier 4 indicated that it would have to contract for at least $460,000 in components from HEC or the bid would have to be withdrawn. Given such situations, HEC does not require that contracts be awarded strictly to the lowest bidders. In determining the contract awards, HEC has established the following goals, in order of priority: Total purchases must not exceed $3,000,000 Provide supplier 4 with sufficient contract requirements that their bid is not withdrawn. Limit total contracts with any supplier to $980,000. Maintain the long-standing relationship with supplier 1 by providing it with a total contract amount of at least $900,000. a. Formulate a linear programming model that can be used to determine the number of units of components, by type, contracted with each supplier to best achieve the goals of Harrison Electronics Corporation. b. Determine the optimal contract plan using the Management Scientist software, including the quantity of each component from each supplier, the total cost of the contract plan developed, and the levels of goal achievement. c. Provide a complete narrative that explains the Management Scientist solution used and the evidence of goal achievement or failure indicated. 2. Hathaway Manufacturing Company Hathaway Manufacturing Company is developing the monthly production plan for three of its products: Product A, Product B, and Product C. The fabricating department can complete 10
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units of Product A in 1 hour, or 15 units of Product B. A unit of Product C can be fabricated in 5 minutes. The department has 250 hours available for the month to be scheduled for these products with overtime available at an additional cost of $15 per hour. Each of the products requires time in the paint department with each unit of Product A needing 20 minutes, each unit of Product B needing 24 minutes, and each unit of Product C needing 30 minutes for the painting operation. There are 1,500 hours currently available in the paint department to be scheduled for these products. Overtime is not available in the paint department. The company has determined that it cannot sell more than 3,000 units of all of the products combined in the planning month. It has been the company's policy to produce at least 200 units of Product B each month.The products' unit contributions to profit are $20, $28, and $40 for products A, B, and C, respectively. The company's goals, in order of importance, are: A monthly profit contribution level for the combination of these products manufactured of at least $120,000. The use of overtime in the fabricating department in the month should be limited to a cost of not more than $1,000 Hours scheduled in the paint department should not exceed 1,200. A minimum of at least 200 units of Product B should be produced. a. Formulate a linear programming model that can be used to determine the optimal production schedule that will best achieve the company's goals. b. Determine the optimal production schedule for Hathaway Manufacturing Company using the Management Scientist software, including the quantity of the products produced, the hours of production utilized, and the levels of goal achievement. c. Provide a complete narrative that explains the Management Scientist solution used and the evidence of goal achievement or failure indicated. 3. ComPro Corporation ComPro Corporation specializes in the assembly, sale, and installation of Dell, Inc. desktop computers to colleges and universities in the Southwestern United States. Compro ships the computers from three distribution centers located in Richmond, Virginia; Atlanta, Georgia; and Washington D.C. Four universities have ordered computers that must be delivered and installed before the end of the fall semester. The schools, Texas Tech; Texas A&M; Florida State; and North Carolina Central, require 520, 250, 400, and 380 units respectively, of the same model and installation configuration. The shipping and installation costs per computer from each of the distribution facilities to each school are given below: Texas Tech Texas A&M Florida State NC Central Richmond $22 $17 $30 $18 Atlanta 15 35 20 25 Washington D. C. 28 21 16 14 ComPro has 420 units of the required model at its Richmond facility, 610 units at the Atlanta facility, and 340 units at the Washington facility. Given that demand for these units exceeds the available supply, ComPro has determined that it can satisfy slightly less than 90% of the demand from customers at an optimal total minimum transportation/installation cost of $22,470. To deflect some of the service concerns expected from customers, ComPro has elected to
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