Develop a linear programming optimization model to determine the distribution plan (from factories to projects) that minimizes the total transportation cost. (Do NOT solve the model.)
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1. Ethan Steel, Inc. has two factories that manufacture steel components for two different rail projects located at two different sites. They would like to determine the number of steel components they need to transport from each factory to each project site. The demand for the steel components for the two projects, Project A, and Project B are 3000, and 4000, respectively. The production and shipping details are as below:
Production details:
Factory 1
2
Maximum capacity 2000
5000
Shipping details (with per-unit shipping cost in dollars):
Project Factory A B 178
265
Develop a linear programming optimization model to determine the distribution plan (from factories to projects) that minimizes the total transportation cost. (Do NOT solve the model.)
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- The Executive Furniture Corporation, which manufactures office desks at three locations: Des Moines, Evansville and Fort Lauderdale. The firm distributes the desks through regional warehouses located in Albuquerque, Boston and Cleveland. The production costs per desk are the same at each factory and hence the only relevant costs are those of shipping from each source to each destination. They are assumed to be constant regardless of their volume shipped. An estimate of the monthly production capacity at each factory and estimate of the number of desks required per month at each destination and the shipping cost ($) per desk from each source to each destination is given in the following table: Transportation table for Executive Furniture Corporation To From Albuquerque Boston Cleveland Factory capacity Des Moines 6 5 8 300 Evansville 5 9 8 400 Fort Lauderdale 4 5 6 350 Requirements 350 250 450…A semiconductor manufacturer produces a particular solid-state module that it supplies to four different television manufacturers. The module can be produced at each of the corporation's three plants, although the costs vary because of differing production efficiencies at the plants. Specifically, it costs 110 units to produce a module at plant A, 95 units at plant B and 103 units at plant C. Monthly production capacities of the plants are 7500, 10000, and 8100 modules, respectively. Sales forecasts project monthly demand at 4200, 8300,6300 and 2700 modules for television manufacturers I, II, III and IV respectively. If the cost for shipping a module from a factory to a manufacturer is as shown below, find a production schedule that will meet all needs at minimum total cost. II II IV 1 13 9. 19 В 1 16 1 14 2 13 1 15 4Answer the following questions after reviewing the problem. 4. Problem 5.17: American Football. The offensive coordinator for the Chicago Bears professional football team is preparing a game plan for the upcoming game against the Green Bay Packers. A review of game tapes from previous Bears–Packers games provides data on the yardage gained for run plays and pass plays. Data shows that when the Bears run against the Packers’ run defense, the Bears gain an average of 2 yards. However, when the Bears run against the Packers’ pass defense, the Bears gain an average of 6 yards. A similar analysis of pass plays reveals that if the Bears pass against the Packers’ run defense, the Bears gain an average of 11 yards. However, if the Bears pass against the Packers’ pass defense, the Bears average a loss of 1 yard. This loss, or negative gain of −1, includes the lost yardage due to quarterback sacks and interceptions. Develop a payoff table that shows the Bears’ average yardage gain for each…
- 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 $175,000 20,000 Toledo $300,000 30,000 Denver $375,000 40,000 Kansas City $500,000 10,000 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 20,000 Atlanta 30,000 Houston 20,000 The shipping cost per unit from each plant to each distribution center is as follows: Distribution Centers Plant…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 $175,000 20,000 Toledo $300,000 30,000 Denver $375,000 40,000 Kansas City $500,000 10,000 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 20,000 Atlanta 30,000 Houston 20,000 The shipping cost per unit from each plant to each distribution center is as follows: Distribution Centers Plant…The Palestinian ministry of sports has four basketball games on a particular night. The ministry wants to assign four teams of officials to the four games in a way that will minimize the total distance traveled by the officials. The supply is always one team of officials and the demand is for only one team of officials at each game. The distances in km for each team of officials to each game location are shown in the following table officials 1 2 3 a 100 150 120 b 130 210 90 c 120 170 90 A) Formulate this problem as Assignment Model (the objective function and constraint equations for the demand and supply) . b) Use QM to solve the Model.
- A rapidly expanding company is looking to lease a small plant in Memphis, Tennessee, Biloxi, Mississippi, or Birmingham, Alabama. Prepare a cost benefit study for each of the three locations using the following data: The annual construction, facilities, and administration expenses for Memphis, Biloxi, and Birmingham will be $40,000, $60,000, and $100,000, respectively. In Memphis, labour and materials are estimated to cost $8 per month, $4 in Biloxi, and $5 in Birmingham. The Memphis site would add $50,000 a year to device transportation expenses, the Biloxi location would add $60,000 per year, and the Birmingham location would add $25,000 per year. The annual production is expected to be 10,000 units.A concrete company transports concrete from their three plants in Nyanyano.- town, Feteh. -town and Tuba.- town to their three construction sites in Ofaakor.- site, Papaase.- site and Krodua. -site. The supply capacities of the three plants, the demand requirements at the three sites, and the transportation costs per ton are as follows: Construction Site Plant O.- site P.- site K. -site Supply(tons) N. town GHs 8 GHs 5 GHs 6 GHs 120 F. town 15 10 12 80 T. town 3 9 10 80 Demand(tons) 150 70 100 280 XXXa) Establish the decision variables for this transportation problem. XXXb) Develop a network graph showing all costs and decision variables. c) i. Formulate the mathematical model that will be used to solve the problem on a computer ii. Fine the initial feasible solution using the Northwest Corner Rule and the total cost. PLEASE ANSWER ONLY C i and C ii PART OF THE QUESTION.A&B Transport Co. is a company that manages a food supply chain. The problem involves the delivery of cargo (canned peas) from four canneries (loading ports) to three destination ports, using tankers. Since the shipping costs are a major expense for the company, management is initiating a study to reduce them as much as possible. For the upcoming season, has come up with an estimation of the available output from each cannery. Furthermore, each destination port has also specific requirements for the total supply of peas that have to be satisfied. This information (in units of tanker loads), along with the shipping cost per tanker load for each loading - destination port combination, is given in Tables 1 and 2. The problem for the A&B Transport Co. is to determine the shipping strategy given the various loading - destination port combinations, so that the total shipping costs are minimised. Question 1 . A&B Transport Co is thinking of including in its strategy the shipment…
- The Thor International Company operates four factories that ship products to five warehouses. The shipping costs, requirements, and capacities are shown in the tableau below. Use the transportation method to find the shipping schedule that minimizes shipping cost. Factory Shipping Cost per Case to each Warehouse Capacity W1 W2 W3 W4 W5 Dummy F1 $4 $5 $4 $3 $6 $0 50,000 F2 $3 $4 $4 $5 $7 $0 80,000 F3 $3 $4 $5 $3 $5 $0 90,000 F4 $4 $6 $5 $6 $3 $0 40,000…The north-south highway system passing through Albany, New York can accommodate the capacities shown in the table below. From To Capacities 1 2 3 1 3 6 1 4 3 2 4 2 2 5 4 3 4 3 3 6 2 4 2 2 4 3 3 4 5 2 4 6 3 5 2 4 5 4 2 5 6 6 How many units go from Node 1 to 3 and 4 to 2, respectively, in order to maximize the flow. a. 5 and 1. b. 5 and 2. c. none of the answers proposed apply d. 6 and 1. e. 6 and 2.KCS Ltd has got three production lines with the same production costs namely; K, L, and S whose production capacities are 140, 160, and 200 units respectively. These are marketed through four destinations B, C, J, and M having demands of 110, 150, 140, and 100 units respectively. The transportation cost between the production lines and market destinations are; K to B, K to C, K to J, K to M, L to B, L to C, L to J, L to M, S to B, S to C, S to J, and S to M as 18, 11, 13, 29, 19, 25, 15, 28, 24, 27, 19, and 12 respectively all costs are US dollars. a).Create a working table taking lines as rows and destinations as columns b). Determine the Cheapest route and Most expensive route to use c).Use the Northwest Corner Method to distribute the products d).Vogel’s Approximation Technique e).Compute their respective total costs incurred