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Solve the following transportation problem: A company has refinery plants that produce gasoline with the following...

  1. Solve the following transportation problem: A company has refinery plants that produce gasoline with the following capacities
  • Houston: 27000 gallons per day
  • New Mexico: 35000 gallons per day

The company supplies the following states:

  • California: 32000 gallons per day
  • Louisiana: 12000 gallons per day
  • Mississippi: 15000 gallons per day

Following are the transportation costs per gallon between each refinery and each customer.

Distribution centers

Plants

California

Louisiana

Mississippi

Houston

0.75

0.40

0.65

New Mexico

0.50

0.70

0.80
  1. Build a transportation network
  2. Write down a linear program that optimizes transportation
  3. Solve the lp and explain its solution
math   Statistics-And-Probability   
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Answer #1

Solutjion From given dada, neny a plonts cal ia ouisiana Mwwipp 0 40 0、65 Hao 0、70 0% Meo 50 15 0.50 x H and N Housbn and HeoMi Coveve -the gaine sappho iom Caltfomta, louisiona and Hivispicol iivolved in SAg gline Supplying efinan veceiviо au ion 어 ineau And Aalag denard ะ ฉ7,cc) +35cco-62.cco Since, demand ofnel tos with Ca (0/0) am Colum Houston 0 0 04 o.8 Volume o goline hauore to eac cell.Prob ven Probem h demand -e, 23.000) (.tala, JFF, (cali6rnia Con Paide uP.to驭.coSahons ofgaoh) Ý,thfY3+%-35,00 ín Mobile should ke a udlo tk blo 31,000- Xary2 12,000 - - -- lauiSian Can tYco.MRppi Con Provrde upo 15/oo gllosfe) Remaining volume of (62,000-5 cco-3m)skald beal Ho h dny cell)Solution of the linear program: Enter the values of different variables, constraints and objective in excel sheet as shown below: 0 Similarly, F6, G6, H6 and l6 represents the volume of supplies to Mobile F7, G7, H7 and17 represents the total supply by California, Louisiana, Missisaippiand the dummy cell Similarly, J5and J6 represents the total supplies for Houston and Mobile FS, G5, H5 and15 represents the volume of supplies to States New Maxico F11, G11, H11, 11, F12, G12, H12 and 112 represenets the total transporation cost for a givencell 2000 1200015000 3000 10 11F14 isformulated as FSF11 It 12 represents the transporation cost States Cal Lousiana M Column 0.4 0.7 0.65 0.8 0.75 New Maxico 0.5 nvolved in sending the goods from California to Houton. Lousiana Mis Column Similarly othercells are formulated. 0.75 0.4 0.7 0.65 New Maxico 0.5 16 17 Cost Cell G17 representsthetotal cost involved in the transporation of gasoline. It is formulatedas 14+G14+H14+114+F15+G15+H15+115 20 21Now, enter the values of variables, constraints, and objectives in Excel Solver, as shown below: Solver Parameters G$17 Set Objective To: Max Ry Changing Variable Cells: Value Of F$5:$I$6 Subject to the Constraints: Add Change Delete Reset All Make Unconstrained Variables Non-Negative Select a Solving Method: Simplex LP Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are HelpAfter putting the values of objective, constraints and variable in the abovewindow, click on Solve tab to get the desired results, as follows Similarly, F6, G6, H6 and 16 representsthe volume of suppliesto Mobile 7,G7, H7and 17 represents the total supplyby California, Louisiana, Missisaippi and the dummy cell Similarly, J5and J6 represents the total supplies for Houston and Mobile F5, G5, H5 and I5 represents the volume of supplies to Houston Houston New Maxico 2700027000 35000 | 35000 F11, G11, H11, 111, F12, 612, H12 and 112 represenets the total transporation cost for a givencell 32000 32000 12000 15000 32000 12000 3:000 15000 F14 is formulated as FS F11. It 11represents the transporation cost States California Lousiana Mis 0.75 0.65 involved in sending the goods from Californiato Houton. New Maxico 0.5 0.7 Similarlyothercells are formulated. 13 California Lousiana Mis Column 7800 2400 15 16 17 New Maxico Cost 31000 Cell G17 represents the total cost involved in the transporation of gasoline. It is formulated as 14+614+H14+114+F15+G15+H15+11 21 Hence, minimum transportation cost involved in this process would be S31,000

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