(a) Use the northwest corner rule to obtain an initial BF solution, and then solve this problem manually by the transportation simplex method. (Keep track of your time.) (b) Reformulate this problem as a general linear programming problem, and then solve it manually by the simplex method. Keep track of how long this takes you, and contrast it with the computation time for part (a).
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- Seas Beginning sells clothing by mail order. An important question is when to strike a customer from the companys mailing list. At present, the company strikes a customer from its mailing list if a customer fails to order from six consecutive catalogs. The company wants to know whether striking a customer from its list after a customer fails to order from four consecutive catalogs results in a higher profit per customer. The following data are available: If a customer placed an order the last time she received a catalog, then there is a 20% chance she will order from the next catalog. If a customer last placed an order one catalog ago, there is a 16% chance she will order from the next catalog she receives. If a customer last placed an order two catalogs ago, there is a 12% chance she will order from the next catalog she receives. If a customer last placed an order three catalogs ago, there is an 8% chance she will order from the next catalog she receives. If a customer last placed an order four catalogs ago, there is a 4% chance she will order from the next catalog she receives. If a customer last placed an order five catalogs ago, there is a 2% chance she will order from the next catalog she receives. It costs 2 to send a catalog, and the average profit per order is 30. Assume a customer has just placed an order. To maximize expected profit per customer, would Seas Beginning make more money canceling such a customer after six nonorders or four nonorders?Instructions: Solve using Excel Solver. Create the linear programming model and get the optimal solution to the problem. (Follow the steps and format in the photo below) 1. A company manufactures two products X1 and X2 on three machines A, B, and C. X1 requires 1 hour on machine A and 1hour on machine B and yields a revenue of Php 30. Product X2 requires 2 hours on machine A and 1 hour on machine B and 1 hour on machine C and yields revenue of PhP 50. In the coming planning period the available time of three machines A, B, and C are 2000 hours, 1500 hours and 600 hours respectively. Find the optimal product mix.PLEASE USE EXCEL Paul Bergey is in charge of loading cargo ships for International Cargo Company(ICC) at the port in Newport News, Virginia. Paul is preparing a loading plan for an ICC freighter destined for Ghana. An agricultural commodities dealer wants to transport the following products aboard this ship.Commodity Amount Available Volume per Ton Profit per Ton (tons) (cubic feet) ($) A 4,800 40 70B 2,500 25 50C 1,200 60 60D 1,700 55 80 Paul can elect to load any and/or all of the available commodities. However, theship has three cargo holds with the following capacity restrictions.Cargo Hold…
- Consider the following linear programming model: maximize Z = 3x1 + 2x2 subject to : x1 +x2 ≤ 1 x1 + x2 ≥ 2 x1,x2 ≥ 0 a) Write this model in a standard (augmented) form. (i.e. Introduce slack/surplus, artificial etc.)b) Constract the initial simplex tableau and carry on your calculations to solve this model using the simplex method. Interpret your result.Show your step-by-step process using THE SPECIAL PURPOSE LINEAR PROGRAMMING: MODI TRANSPORTATION METHOD to solve this problem. XYZ Incorporated has received a contract to supply gravel to three new road projects located at three different locations. Project A needs 174 truckloads, Project B needs 204 truckloads, and Project C needs 143 truckloads. The company has three gravel warehouses located in three different places. Warehouse 1 has 158 truckloads available, warehouse 2 has 184, and warehouse 3 has 179. The cost of transportation from the warehouse to the projects are: from warehouse 1 to Projects A, B, C = Php 4, Php 8, Php 8 per truckload respectively. From warehouse 2 to Projects A, B, C = Php 16, Php 24, Php 16 per truckload respectively. From warehouse 3 to Projects A, B, C = Php 8, Php 16, Php 24 per truckload respectively. The objective is to design a plan of distribution that will Minimize the cost of transportation.Formulate the strong duality theorem and show its application to the following LP problem. Hint: find the dual of this given primal LP problem and solve both problems using graphical (geometrical) approach. Analyze the obtained solutions in terms of the strong duality theorem. Please show all work, this is an ungraded review question from lecture.
- 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…The director of Burtonsville Civil Defense Agency has been ordered to draw up a disaster plan for assigning casualties to hospitals in the event of a serious earthquake. For simplicity, we will assume that causalities will occur at two points in the city and will be transported to three hospitals. It is estimated that there will be 300 casualties at point A and 200 at point B. Travel times to hospitals 1, 2, and 3 are 25, 15, and 10 minutes, respectively; from point B they are 20, 5, and 15 minutes. Hospital capacities for emergency cases are 250, 150, and 150 patients. How should the victims be assigned to hospitals to minimize the total time lost in transporting them? Disaster Point Hospital Total Casualties 1 2 3 A 25 15 10 300 B 20 5 15 200 Maximum Capacity 250 150 150 Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You…The distance between two cities in the United States can be approximated by the following formula, where lat1 and long1 are the latitude and longitude of city 1 and lat2 and long2 are the latitude and longitude of city 2. 69 (lat1 − lat2)2 + (long1 − long2)2 Ted's daughter is getting married, and he is inviting relatives from 15 different locations in the United States. The file Wedding gives the longitude, latitude, and number of relatives in each of the 15 locations. Ted would like to find a wedding location that minimizes the demand-weighted distance, where demand is the number of relatives at each location. Assuming that the wedding can occur anywhere, find the latitude and longitude of the optimal location. (Hint: Notice that all longitude values given for this problem are negative. Make sure that you do not check the option for Make Unconstrained Variables Non-Negative in Solver. Round your answers to three decimal places.) latitude of the optimal wedding location:…
- A company needs to locate three departments (I, II, and III) in the three areas (A, B, and C) of a new facility. They want to minimize interdepartmental transportation costs, which are expected to be $.40 per load per meter moved. An analyst has prepared the following distances and flow matrices: Distance (meters) Flows (loads per week) From/To A B C From/To I II III A - 30 40 I - 30 110 B - 60 II 90 - 70 C - III 70 60 - In what areas, A, B, and C, should departments I, II, and III be located that minimize the total cost of moving loads over…The following table presents cost, capacity, and demand data for a transportation problem in Stephanie Robbin’s furniture company. Set up the appropriate transportation table and find the optimal solution using Excel's solver. From/To 1 2 3 Supply A 30 10 5 20 B 10 10 10 30 C 20 10 25 75 Demand 40 60 55 a. Is the problem balanced? [ Select ] ["Yes", "it is balanced", "No", "cannot determine"] , If not, where? [ Select ] ["Neither", "Supply", "Demand"] , and by how much? [ Select ] ["0", "40", "30", "25"] b. What is the optimal cost? $ [ Select ] ["2,500", "1,100", "1,275", "1,300"] c. Were you able to meet all demand requirement? [ Select ] ["no", "cannot determine based on the information given", "yes"] If not, which destination (s) was/were not met? [ Select ] ["none, all destinations were met based on supply and demand being equal", "destination 3 by 30 units", "destination 2 by 30 units", "destination 1 by 25 units…The Easy Time Grocery chain operates in major metropolitan areas on the East Coast. The stores have a “no-frills” approach, with low overhead and high volume. They generally buy their stock in volume at low prices. However, in some cases they actually buy stock at stores in other areas and ship it in. They can do this because of high prices in the cities they operate in compared with costs in other locations. One example is baby food. Easy Time purchases baby food at stores in Albany, Binghamton, Claremont, Dover, and Edison and then trucks it to six stores in and around New York City. The stores in the outlying areas know what Easy Time is up to, so they limit the number of cases of baby food Easy Time can purchase. The following table shows the profit Easy Time makes per case of baby food, based on where the chain purchases it and at which store it is sold, plus the available baby food per week at purchase locations and the shelf space available at each Easy Time store per week:…