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# (a) Formulate a linear programming problem to minimize total cost for this transportation problem.(b) Solve the linear programming formulation from part (a) by

Nashville     Miami         Charleston        Supply
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Tucson                        900         1200             500                  25
Seattle                        650          1050            700                   25
Baltimore                    550           815             472                  10
Detroit                        620           905              514                  25
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Demand                      40             20                 25

### 1 Answer by Expert Tutors

Deanna L. | Electrical engineering major and music lover with MIT degreeElectrical engineering major and music l...
4.9 4.9 (131 lesson ratings) (131)
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Manaal!  there's a really cool method that does not require a calculator. the goal into meet demand and still fit the supply limits. We called it NW corner method. You need excel to determine the cost but here is how it works:
1) start on the top left hand corner.
2) find the smallest cost across the first row: 500.
3) use tuscon's supply to meet Charleston's demand: 25.
4) draw a line through Tuscon and Charleston: horizontal and vertical.
5) find the next open NW corner and fin the lowest in the available row: 650 with Seattle meeting nashville's demands.
6) use seattle's supply to meet nashville's demands:25.
7) cross out Seattle  as a supply port with horizontal line. Then cross out the demand of 40 for Nashville, subtract 25, and write in 15. 15 left for Nashville!
8) find the next NW corner and find te lowest in the available row: 550 using baltimore's supply to meet nashville's demand.
9) use baltimore's supply to fill nashville's demand: 10.
10) cross out Baltimore as a supply port with a horizontal line. Cross out the remaining demand for Nashville, subtract ten, an write in five left for demand.
11) find the next open NW corner left and identify the lowest cost:620.
12) use detroit's supply to meet the remaining five of nashville's needs.
13) cross out Nashville as a demand with a vertical line.
14) cross out the supply at Detroit, subtract 5, write in 20.
15) find the next NW corner: 905 with Miami as open demand unmet.
16) use detroit's last 20 units to meet miami's demand.

So that means 25*500+650*25+10*550+5*620+20*905 is the minimized cost. There's variations of this called vogel's cost that may net something lower. So let me know if you're interested in that too.