Fouke has three plants, one each in Orlando, Atlanta and Lexington each. Their capacities are 225,000 units, 175,000 units and 187,500 units respectively. Fouke needs to ship couches from these plants to 12 demand locations. The transportation cost between each source and destination is given to you in the Excel file below. How can you minimize transportation cost?

1. As is, the optimal total cost?

2. Which supply constraints are binding? (select all that apply)

A. Orlando

B. Atlanta

C. Lexington

3. Which of the market constraints are binding (demand constraints)? (Select all that apply)

Ral/Durham

Charleston

Miami

Columbus

Tampa

Birmingham

Greens/WS

Columbia

Savannah

Atlanta

Orlando

Knoxville

4. How many dimensions does the associated polygon exist in?

5. How many lines (or sides) does the corresponding polygon have including the non-negative constraints?

6. If you change the Knoxville demand to 100,000, what is the new total cost?

7. Now, return Knoxville's demand to 77,640. Resolve it and run the sensitivity report to get the shadow prices. What is the shadow price associated with the supply constraint on Atlanta's supply of 175,000? (Give the answer to 2 decimal places.)

8. Looking at the sensitivity report, adding an extra demand to which city would be most detrimental to your total costs?

Tampa

Ral/Durham

Atlanta

Orlando

Charleston

Knoxville

Birmingham

Columbus

Columbia

Miami

Savannah

Greens
 

A 1 2 3 Costs per unit 4 MARKETS 5 6 Atlanta 7 8 Charleston 9 Columbia 10 Columbus 11 Greems/W.S. 12 Knoxville 13 Miami 14 Orlando 15 Ral./Durham 16 Savannah 17 Tampa 18 19 Birmingham B C Orlando 5.72 6.45 5.53 6.18 56.85 7.89 8.29 4.34 0.66 8.82 20.21 1.38 D E Atlanta Lexington 0.66 1.97 3.8 2.63 14.62 4.61 2.54 8.62 5.72 4.89 15.16 5.92 4.61 6.58 3.62 2.63 74.71 0.66 2.89 12.24 7.89 1.97 28.87 9.47 F G H DEMAND Atlanta Birmingham Charleston Columbia Columbus Greems/W.S. Knoxville Miami Orlando Ral./Durham Savannah Tampa J 89179 17750 8093 24604 5339 5339 77640 19316 109902 37900 6493 86799 K L Supply Orlando Atlanta Lexington M 225000 175000 187500 N