Suppose the total flow into a node of a network isrestricted to 10 units or less. How can we represent thisrestriction via an arc capacity constraint? (This still allowsus to use the Ford–Fulkerson method to find the maximumflow.)
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Suppose the total flow into a node of a network is
restricted to 10 units or less. How can we represent this
restriction via an arc capacity constraint? (This still allows
us to use the Ford–Fulkerson method to find the maximum
flow.)
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- I need help with the constraint and how to solve the probelm on excelConsider the maximum flow problem shown above, where the source is node S, the sink is node T, and the arc capacities are the numbers shown next to these directed arcs. Use excel to solveA company supplies goods to three customers, who eachrequire 30 units. The company has two warehouses.Warehouse 1 has 40 units available, and warehouse 2 has 30units available. The costs of shipping 1 unit from warehouseto customer are shown in Table 7. There is a penalty for eachunmet customer unit of demand: With customer 1, a penaltycost of $90 is incurred; with customer 2, $80; and withcustomer 3, $110. Formulate a balanced transportationproblem to minimize the sum of shortage and shipping costs.
- A steel production plant manufactures bands and coils which sell at a profit of $25 and $30 per ton,respectively. The production rate of the plant for bands is 200 tons/hr, and that for coils is 140 tons/hr.Based on the market analysis, it has been identified that the weekly demand is at most 6000 tons and4000 tons for bands and coils, respectively . The plant operates for a maximum of 40 hours per week. 1. In Microsoft Excel, formulate a linear programming model instance for this problem, then solve. 2. Assume that the products need to be painted after manufacturing, and the painting departmentcan paint at a rate of 600 tons per hour for bands and 400 tons per hour for coils. The paintingdepartment works only for 20 hours. Update the linear programming model instance to accom-modate this requirement, and re-solve the problem. 3. The plant is planning to introduce another product “rods” to its production mix with the followingparameters:•Profit/ton = $40•Production volume = 150…Jim Jones manufactures inexpensive set-it-up-yourself furniture for students. He currently makes two products – bookcases and tables. Each bookcase contributes $24 to profit, and each table, $20. Each product passes through two manufacturing points, cutting and finishing. Bookcases take 4 hours a unit in cutting and 4 hours in finishing. Tables require 3 hours a unit in cutting and 5 in finishing. There are currently 40 hours available in cutting and 50 in finishing. Determine the optimum solution. Use graphic linear programming to find the product mix that produces the maximum profit for Jim.What function does linear programming play in OR?
- VVH wants to determine the optimal case mix for diagnosis-related groups(DRGs) that will maximize profits. Limited resources (e.g., space, qualified employees) are available to serve patients classified in the various DRGs, and minimum levels of service (number of cases) must be achieved for each DRG. (1) Formulate linear optimization problem. Is non-negativity constraint required in this problem?The starting node of the shortest path problem has a supply out flow value of -1 in the LP model. True False (Don't hand writing solution)1. Transshipment ProblemThe Northside and Southside facilities of Zeron Industries supply three firms (Zrox,Hewes, Rockrite) with customized shelving for its offices. They both order shelvingfrom the same two manufacturers, Arnold Manufacturers and Supershelf, Inc. Currently weekly demands by the users are 50 for Zrox, 60 for Hewes, and 40 forRockrite. Both Arnold and Supershelf can supply at most 75 units to its customers.Because of long standing contracts based on past orders, unit costs from themanufacturers to the suppliers are: Zeron N Zeron S Arnold 5 8 Supershelf 7 4The costs to install the shelving at the various locations are: Zrox Hewes Rockrite Zeron N 1 5 8 Zeron S 3 4 4 How should Zeron…
- . A refiner in city Q serves four customers near city W and maintains consignment inventory (owned by the refiner) at each location. Currently, the refiner uses TL (truckload) transportation to deliver separately to each customer. Each truck costs $(759) plus $(309) per stop. The refiner is considering aggregating deliveries to city W on a single truck. The demand of the first customer is 75 tons a year, the demand of the second customer is 30 tons per year, and the demand of the third and fourth customers is 10 tons per year. The product cost is $8,000 per ton, and it uses a holding cost of (24)%. The truck capacity is 20 tons. a. What is the optimal delivery policy to each customer if the refiner ships separately to each of them? What is the annual total inventory-related cost? b. What is the optimal delivery policy to each customer if the refiner aggregates shipments to each of the four customers on every truck that goes to city W? What is the annual total inventory-related cost?…Search for the best solution of the following integer program using the branch and bound algorithm.Discuss the five (5) steps of the Theory of Constraints and apply each to asimulation/assumption of a constraint impacting Jaguar.