| A company produces window blinds at its Los Angeles, Atlanta, and New York facilities. Each...

 

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| A company produces window blinds at its Los Angeles, Atlanta, and New York facilities. Each month, the Los Angeles plant can produce up to 100,000 units of blinds. Atlanta can produce up to 120,000 units, and New York can produce up to 140,000 units. Each month, the company must ship to the four distribution regions of the United States-East, Midwest, South, and West-as shown in the table below. For example, the West region must receive at least 130,000 units each month. The cost of manufacturing a unit at each plant and shipping a unit to each region of the country is given in the table. The company wants to find how many units should be shipped from each plant to each region of the country to minimize the total production and transport costs. Plant Los Angeles Atlanta New York city Demand Manufacturing and Transportation cost ($/unit) Midwest South West c. d. East 15.00 13.20 12.50 90,000 13.50 12.60 13.10 60,000 14.20 11.80 13.30 60,000 12.20 14.80 15.40 130,000 Capacity 100,000 120,000 140,000 a. Develop a linear programming model (not just a spreadsheet or the LPSolve model) where you list every decision variable and what they represent as well as every parameter or input and what they mean. b. Solve the model using LPSolve, Excel, or any other MILP Solver. What is the cheapest way ship blinds to get each region? What is the total cost? If the production and transportation cost at Los Angeles plant increases by $1 per unit, would it change the solution in (b)? Explain your answer. | A company produces window blinds at its Los Angeles, Atlanta, and New York facilities. Each month, the Los Angeles plant can produce up to 100,000 units of blinds. Atlanta can produce up to 120,000 units, and New York can produce up to 140,000 units. Each month, the company must ship to the four distribution regions of the United States-East, Midwest, South, and West-as shown in the table below. For example, the West region must receive at least 130,000 units each month. The cost of manufacturing a unit at each plant and shipping a unit to each region of the country is given in the table. The company wants to find how many units should be shipped from each plant to each region of the country to minimize the total production and transport costs. Plant Los Angeles Atlanta New York city Demand Manufacturing and Transportation cost ($/unit) Midwest South West c. d. East 15.00 13.20 12.50 90,000 13.50 12.60 13.10 60,000 14.20 11.80 13.30 60,000 12.20 14.80 15.40 130,000 Capacity 100,000 120,000 140,000 a. Develop a linear programming model (not just a spreadsheet or the LPSolve model) where you list every decision variable and what they represent as well as every parameter or input and what they mean. b. Solve the model using LPSolve, Excel, or any other MILP Solver. What is the cheapest way ship blinds to get each region? What is the total cost? If the production and transportation cost at Los Angeles plant increases by $1 per unit, would it change the solution in (b)? Explain your answer.

Answer rating: 100% (QA)

SOLUTION a The decision variables in this linear programming model are the number of units shipped from each plant to each region Let x ij be the numb... View the full answer