For Part B, Select your answers, choices are: , , =

For "Which plants are open", choices are: Detroit and Denver; Detroit and St. Louis; St. Louis and Kansas City; Detroit; Toledo, and Kansas City; Detroit, Toledo, and St. Louis; Detroit, Toledo, and Denver

The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Product is shipped to regional distribution centers located in Boston, Atlanta, and Houston. Because of an anticipated increase in demand, Martin-Beck plans to increase capacity by constructing a new plant in one or more of the following cities: Detroit, Toledo, Denver, or Kansas City. The estimated annual fixed cost and the annual capacity for the four proposed plants are as follows: Proposed Plant Annual Fixed Cost Annual Capacity Detroit $200,000 20,000 Toledo $280,000 20,000 Denver $360,000 10,000 Kansas City $310.000 20,000 The company's long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows: Distribution Center Annual Demand Boston 35,000 Atlanta 25,000 Houston 10,000 The shipping cost per unit from each plant to each distribution center is as follows: Distribution Centers Plant Site Boston Atlanta Houston Detroit 5 2 3 Toledo 4 3 4 Denver 9 7 5 Kansas City 10 4 2 St. Louis 8 4 3 Management wants to run a model that allows for any plant or set of plants to be open so that total cost is minimized. The variable costs for the proposed plant locations are estimated to be the following: Detroit ($4.43), Toledo ($4.32), Denver ($4.64), and Kansas City ($3.88). We need an estimate of the fixed cost and variable cost at the current St. Louis plant. The file StLouisMB contains 15 observations from previous years that will allow us to estimate these. Volume Total Cost 28,800 $452,985 26,200 $453,616 28,700 $457,376 28,100 $458,329 24,300 $431,608 27,000 $444,391 21,000 $426,287 22,300 $438,348 29,500 $463,317 19,300 $413,902 28,600 $455,275 27,300 $450,034 27,900 $454,393 25,800 $452,964 27,200 $454,416 (a) Use simple linear regression, with total cost as the dependent variable (y) and volume as the independent variable (x). The model y = bo + bix will give you estimates of b1 = the per unit variable cost and bo = annual fixed cost. Round the fixed cost estimate to the nearest dollar and the variable cost estimate to the nearest cent. Fixed cost: $ Variable cost: (b) Using the data given above for the proposed locations and the fixed and variable costs for St. Louis estimated in part (a), build an optimization model to minimize total cost to meet demand. If the constant is "1", it must be entered in the box. Let y = 1 if a plant is constructed in Detroit; O if not y2 = 1 if a plant is constructed in Toledo; O if not ; y3 = 1 if a plant is constructed in Denver; O if not y4 = 1 if a plant is constructed in Kansas City; O if not ; O y5 = 1 if a plant is kept in St. Louis; 0 if not Xij = units shipped from plant i to distribution center i where i = 1 (Detroit), 2 (Toledo), 3 (Denver), 4 (Kansas City), 5 (St. Louis) and j = 1 (Boston), 2 (Atlanta), 3 (Houston) Min X12 X13 X21 X22 - X32 X41 X23 X31 X33 X42 X43 - X51 X52 X53 yi - y2 -- y3 y4 ys s.t. X11 - X12 X13 yi - X21 X22 X23 y2 - X31 y3 X41 - X42 y4 X43 X53 Select your answer - - Select your answer - - Select your answer - - Select your answer - - Select your answer - - Select your answer - V - Select your answer - - Select your answer - X51 y5 X11 X21 X31 X41 X51 X12 X22 X32 X42 X52 X13 X23 - X33 X43 X53 Xij 20 for all i and ; 71, 72, 73, 74, y5 (0,1} which plants are open? - Select your answer - What is the total cost to meet demand? Do not round intermediate calculations. If required, round your answer to the nearest dollar. $ The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Product is shipped to regional distribution centers located in Boston, Atlanta, and Houston. Because of an anticipated increase in demand, Martin-Beck plans to increase capacity by constructing a new plant in one or more of the following cities: Detroit, Toledo, Denver, or Kansas City. The estimated annual fixed cost and the annual capacity for the four proposed plants are as follows: Proposed Plant Annual Fixed Cost Annual Capacity Detroit $200,000 20,000 Toledo $280,000 20,000 Denver $360,000 10,000 Kansas City $310.000 20,000 The company's long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows: Distribution Center Annual Demand Boston 35,000 Atlanta 25,000 Houston 10,000 The shipping cost per unit from each plant to each distribution center is as follows: Distribution Centers Plant Site Boston Atlanta Houston Detroit 5 2 3 Toledo 4 3 4 Denver 9 7 5 Kansas City 10 4 2 St. Louis 8 4 3 Management wants to run a model that allows for any plant or set of plants to be open so that total cost is minimized. The variable costs for the proposed plant locations are estimated to be the following: Detroit ($4.43), Toledo ($4.32), Denver ($4.64), and Kansas City ($3.88). We need an estimate of the fixed cost and variable cost at the current St. Louis plant. The file StLouisMB contains 15 observations from previous years that will allow us to estimate these. Volume Total Cost 28,800 $452,985 26,200 $453,616 28,700 $457,376 28,100 $458,329 24,300 $431,608 27,000 $444,391 21,000 $426,287 22,300 $438,348 29,500 $463,317 19,300 $413,902 28,600 $455,275 27,300 $450,034 27,900 $454,393 25,800 $452,964 27,200 $454,416 (a) Use simple linear regression, with total cost as the dependent variable (y) and volume as the independent variable (x). The model y = bo + bix will give you estimates of b1 = the per unit variable cost and bo = annual fixed cost. Round the fixed cost estimate to the nearest dollar and the variable cost estimate to the nearest cent. Fixed cost: $ Variable cost: (b) Using the data given above for the proposed locations and the fixed and variable costs for St. Louis estimated in part (a), build an optimization model to minimize total cost to meet demand. If the constant is "1", it must be entered in the box. Let y = 1 if a plant is constructed in Detroit; O if not y2 = 1 if a plant is constructed in Toledo; O if not ; y3 = 1 if a plant is constructed in Denver; O if not y4 = 1 if a plant is constructed in Kansas City; O if not ; O y5 = 1 if a plant is kept in St. Louis; 0 if not Xij = units shipped from plant i to distribution center i where i = 1 (Detroit), 2 (Toledo), 3 (Denver), 4 (Kansas City), 5 (St. Louis) and j = 1 (Boston), 2 (Atlanta), 3 (Houston) Min X12 X13 X21 X22 - X32 X41 X23 X31 X33 X42 X43 - X51 X52 X53 yi - y2 -- y3 y4 ys s.t. X11 - X12 X13 yi - X21 X22 X23 y2 - X31 y3 X41 - X42 y4 X43 X53 Select your answer - - Select your answer - - Select your answer - - Select your answer - - Select your answer - - Select your answer - V - Select your answer - - Select your answer - X51 y5 X11 X21 X31 X41 X51 X12 X22 X32 X42 X52 X13 X23 - X33 X43 X53 Xij 20 for all i and ; 71, 72, 73, 74, y5 (0,1} which plants are open? - Select your answer - What is the total cost to meet demand? Do not round intermediate calculations. If required, round your answer to the nearest dollar. $