Tobacco is purchased by Cooperative Tobacco Farmers Inc is s

Tobacco is purchased by Cooperative Tobacco Farmers, Inc., is stored in warehouses in four cities at the end of each season.

Location

Capacity (tons)

Charlotte

90

Raleigh

50

Lexington

80

Danville

60

280

These warehouses supply the following amounts of tobacco to companies in the following three cities:

Plant

Demand (tons)

Richmond

120

Winston-Salem

100

Durham

110

330

The railroad shipping costs per ton are as follows:

To

Richmond

Winston-Salem

Durham

Charlotte

$70

100

50

Raleigh

120

90

40

Lexington

70

30

110

Danville

90

50

70

a)      Cooperative Tobacco Farmers wants to determine what amounts of tobacco should be shipped from the warehouses to the tobacco plants at the least total cost.

b)      Because of railroad construction, shipments are presently prohibited from Charlotte to Richmond. How should Cooperative Tobacco Farmers adjust their shipping plans and still minimize cost?

Location	Capacity (tons)
Charlotte	90
Raleigh	50
Lexington	80
Danville	60
	280

Solution

a Location Capacity (tons) Plant Demand (tons) Charlotte 90.00 Richmond 120 Raleigh 50.00 Winston-Salem 100 Lexington 80.00 Durham 110 Danville 60.00 330.00 280.00 Cost matrix From/To Richmond Winston-Salem Durham Charlotte 70.00 100.00 50.00 Raleigh 120.00 90.00 40.00 Lexington 70.00 30.00 110.00 Danville 90.00 50.00 70.00 Decision variable matrix - How much to be shipped from which warehouse to which plant From/To Richmond Winston-Salem Durham Charlotte 30.00 0.00 60.00 Raleigh 0.00 0.00 50.00 Lexington 40.00 40.00 0.00 Danville 0.00 60.00 0.00 Capacity constraints Charlotte 90.00 = 90.00 Raleigh 50.00 = 50.00 Lexington 80.00 = 80.00 Danville 60.00 = 60.00 Demand Constraint Richmond 70.00 <= 120 Winston-Salem 100.00 <= 100 Durham 110.00 <= 110 Objective function - Minimize overall cost of shipping Total cost 14100 Using solver to solve above decision matrix is the solution with the minimum cost being 14100 b Location Capacity (tons) Plant Demand (tons) Charlotte 90.00 Richmond 120 Raleigh 50.00 Winston-Salem 100 Lexington 80.00 Durham 110 Danville 60.00 330.00 280.00 Cost matrix From/To Richmond Winston-Salem Durham Charlotte 100,000.00 100.00 50.00 Raleigh 120.00 90.00 40.00 Lexington 70.00 30.00 110.00 Danville 90.00 50.00 70.00 Since shipment is prohibited from Charlotte to Richmond,so the cost is increased so that there is no shipment for this Decision variable matrix - How much to be shipped from which warehouse to which plant From/To Richmond Winston-Salem Durham Charlotte 0.00 0.00 90.00 Raleigh 30.00 0.00 20.00 Lexington 40.00 40.00 0.00 Danville 0.00 60.00 0.00 Capacity constraints Charlotte 90.00 <= 90.00 Raleigh 50.00 <= 50.00 Lexington 80.00 <= 80.00 Danville 60.00 <= 60.00 Demand Constraint Richmond 70.00 <= 120 Winston-Salem 100.00 <= 100 Durham 110.00 <= 110 Objective function - Minimize overall cost of shipping Total cost 15900 Using solver to solve above decision matrix is the solution with the minimum cost being 15900 There will be no shippment from Charlotte to Richmond