The basic feasible solution to the transportation problem with the costs as shown below are x11, x12, x23, x31, X33, X43, X44 1 2 3 4 Supply 1 9 7 128 18 2 15 12 12 154 3 8 9 6 126 14 |1412 11 1212 Demand 6 14155
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c. Using the basic feasible solution, obtain the multipliers ui and vj for each row and column. Check whether the solution is optimal
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- a.Find the starting solution of this transportation model by Least Cost Method. (15P) (Unit transportation costs are given in the table) D1 D2 D3 D4 Supply M1 16 24 14 11 25 M2 21 18 17 9 30 M3 15 13 21 14 40 Demand 25 25 20 25Oranges are grown, picked and then stored in warehouses in Tampa, Miami, and Fresno.Theses warehouses supply oranges to markets in New York, Philadelphia, Chicago, and Boston.The following table shows the shipping costs per truckload (in hundreds of dollars), supply, anddemand. Because of an agreement between distributors, shipments are prohibited from Miamito Chicago:To (cost, in $100)From New York Philadelphia Chicago Boston SupplyTampa 9 14 12 17 150Miami 11 10 6 10 250Fresno 12 8 15 7 200Demand 110 250 140…Oranges are grown, picked, and then processed and pack-aged at distribution centers in Tampa, Miami, and Fresno. These centers supply oranges to markets in New York,Philadelphia, Chicago, and Boston. The following tableshows the shipping costs per truckload ($100s), supply,and demand: Because of an agreement between distributors, ship-ments are prohibited from Miami to Chicago. Solve this problem. to Newfrom York Philadelphia Chicago Boston SupplyTampa $ 9 $14 $12 $17 300Miami 11 10 6 10 200Fresno 12 8 15 7 250Demand 160 210 130 180
- Find an initial basic feasible solution for a given transportation problem by using Vogel's approximation method D1 D2 D3 D4 Supply S1 11 13 17 14 250 S2 16 18 14 10 300 S3 21 24 13 10 400 Demand 200 225 275 250Dogie Agency has three police dogs to be assigned to 3 different department stores. The cost of each dog on eachdepartment is given below Dogs SM Robinson CSI1 200 350 2702 300 250 1503 400 350 270 1. What quantitative technique can you utilize for this problem? Explain.2. Determine the minimum cost of each dog per department.At the beginning of month t, farmer Smith has xtbushels of wheat in his warehouse. He has the opportunityto sell wheat at a price st dollars per bushel and can buywheat at pt dollars per bushel. Farmer Smith’s warehousecan hold at most C units at the end of each month.a Formulate a recursion that can be used to maximizethe total profit earned during the next T months.b Let ft(xt) be the maximum profit that can be earnedduring months t, t 1, . . . , T, given that xt bushels of wheat are in the warehouse at the beginning of month t. By working backward, show that for appropriately cho-sen constants at and bt, ft(xt) at btxt c During any given month, show that the profit-maximizing policy has the following properties: (1) The amount sold during month t will equal either xt or zero.(2) The amount purchased during a given month will beeither zero or sufficient to bring the month’s endingstock to C bushels.
- We have three Suppliers and four Demanders. the Suppliers have inventory of 61 , 49, 29 respectively, and the Demanders require 54, 37, 4, 44 respectively. Shipping costs from S1 to D1, D2, D3 , D4 are 103, 30, 68, 54from S2 to D1, D2, D3 , D4 are 16, 95, 84, 35from S3 to D1, D2, D3 , D4 are 40, 44, 46, 101. Check that this is a balanced transportation problem. Find the optimal mimimal shipping cost:Two plants supply three customers with medicalsupplies. The unit costs of shipping from the plants to thecustomers, along with the supplies and demands, are givenin Table 42. TAB LE 42ToFrom Customer 1 Customer 2 Customer 3 SupplyPlant 1 $55 $65 $80 35Plant 2 $10 $15 $25 50Demand 10 10 10 a The company’s goal is to minimize the cost of meeting customers’ demands. Find two optimal bfs for thistransportation problem.b Suppose that customer 2’s demand increased by oneunit. By how much would costs increase?Suppose a company must service customers lying inan area of A sq mi with n warehouses. Kolesar and Blumhave shown that the average distance between a warehouseand a customer is An Assume that it costs the company $60,000 per year tomaintain a warehouse and $400,000 to build a warehouse.(Assume that a $400,000 cost is equivalent to foreverincurring a cost of $40,000 per year.) The company fills160,000 orders per year, and the shipping cost per order is$1 per mile. If the company serves an area of 100 sq mi,then how many warehouses should it have?
- Explain how to determine the number of variables and constraints that would be in a transportation problem simplyby knowing the number of sources and the number of destinations.1. Consider the following transportation tableau with three origins and three destinations. To From Windhoek Gobabis Walvis Bay Supply Rundu 4 10 6 100 Oshakati 8 16 6 300 Katima Mulilo 14 18 10 300 Demand 200 300 200 Required Marks Sub total Total Use the Vogel Approximation method (VAM) to find an initial feasible solution? 20 20 To12. XYZ Company is specialized in mangoes distribution in the city of Muscat. Sales are 500 boxes (unit) per month. It costs OR 10 to make and receive an order and holding cost is OR 3.5 per box per year. The prices depend on quantities purchased such that the order quantities from 1 to 199 at a unit price RO 5; quantity 200 to 499 at a unit price 4.5 RO; and quantity 500 and more at a per unit price of 4 RO. If the discount option is considered, then the best decision that minimizes the total annual inventory cost is a. 185 units, Total cost = 30,649 b. 500 units, Total cost = 24,995 c. 200 units, Total cost =27,240 d. None is correct e. 450 units, Total cost = 23,500