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MGT445 Homework Assignment Problems Solution




Question;Problem 1 A chemical company owns four factories that manufacture a certain chemical in raw form. The company would like to get in the business of refining the chemical. It is interested in building refining facilities, and it has identified three possible sites. Table 1 contains variable costs, fixed costs, weeklycapacities for the three possible refining facility sites, and weekly production amounts for each factory. The variable costs are in dollars per week and include transportation costs. The fixed costs are in dollars per year. The production amounts and capacities are in tons per week.Refining sites123Factoryproduction125201510002152520100032015255004251515500Fixed cost500,000500,000500,000Capacity150015001500FactorylocationsTable 1. Cost, capacity, and production information for the chemical company.a) Formulate a linear program that can help identify the facility configuration that minimizes the total costs.b) At each site, the company can also open a smaller size facility with capacity of 750 at a fixed cost of 300,000. If all other information remains the same, formulate a linear optimization model that minimizes the total costs.c) The company has revamped its production process in factory 3. The new process produced better quality product, but has a higher production cost.Suppose the increase in production cost due to the new process is $4 per ton. Then, is the formulation in part (a) still valid? If not, what changes would you suggest?Problem 2Straub Ltd. has five plants running at full capacity in Des Moines, IA, Racine, WI, Gary, IN, Kalamazoo, MI, and Duluth, MN. These plants supply four distribution warehouses in St. Paul, MN, Milwaukee, WI, Chicago, IL and Detroit, MI. The following table specifies the transportation cost per unit from each plant to distribution warehouse.The next table specifies the production capacity of each plant and the demand at each warehouse.a) Formulate a linear program to determine the distribution plan that minimizes the total costs.b) Recently, the state of Michigan has imposed a new tariff that impacts all inter? state traffic that arrives in Michigan. For Straub Ltd., the tariff increases the cost of shipments to Michigan from other states by $2. How does this change impact the model formulation in part (a)?Problem 3Consider a company that faces the following demand over the next six months??? 45000, 55000, 70000, 100000, 80000, and 60000. The company has a patented production process that requires special components. The cost of materials is $5 per unit. The cost of holding inventory is $1.25 per unit per month and inventory is assessed based on the amount held at the end of the month. The companybacklogs its demand and the cost of backlogging is $2 per unit per month. Hiring and training a new worker costs $200 per worker and firing a worker costs $250 per worker. The company has a starting inventory of 2500 units and an ending inventory target (at the end of six months) of 4500 units. The number of working days in the upcoming months is 20 per month. The product requires 0.15 laborhours per unit. Each worker is paid $8 per hour. The working day consists of a single 8?hour shift.a) Evaluate the cost of the ?chase? strategy.b) Evaluate the cost of the ?level? strategy.c) Assuming that backlogging is not allowed, formulate a linear program to determine the optimal aggregate production plan.


Paper#46075 | Written in 18-Jul-2015

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