Module C Internet Homework Problems

C.18 The following table presents cost, capacity, and demand data for a transportation problem in Stephanie Robbin’s furniture company. Set up the appropriate transportation table and find the initial solution using northwest-corner data. Note that a “dummy” source is needed to balance the problem.

From \ To / 1 / 2 / 3 / Capacity
A / $30 / $10 / $5 / 20
B / $10 / $10 / $10 / 30
C / $20 / $10 / $25 / 75
Demands / 40 / 60 / 55

C.19 Determine whether the new solution table presented in Example C4 (see Figure C.8 in the text) contains the optimal transportation allocation for Arizona Plumbing. If not, compute an improved solution and test it for optimality.

C.20 After one iteration of the stepping-stone method, G. W. Willis Paint Company produced the following transportation table. Complete the analysis, determining an optimal shipping solution.

G.W. Willis Paint Company

From \ To / Warehouse 1 / Warehouse 2 / Warehouse 3 / Factory capacity
Factory A / $ 8
120 / $ 5 / $ 6 / 120
Factory B / $ 15
/ $ 10
80
/ $ 14
/ 80
Factory C / $ 3
30 / $ 9 / $ 10
50 / 80
Warehouse
requirements / 150 / 80 / 50 / 280

Cost = $2,350

C.21 Sound Track Stereos assembles its high-fidelity stereophonic systems at three plants and distributes them from three regional warehouses. The production capacities at each plant, demand at each warehouse, and unit shipping costs are presented in the following table:

Sound Track Stereos

From \ To / Warehouse APlant supply / Warehouse BWarehouse B / Warehouse C / Plant Capacity
Plant W / $6 / $4 / $9 / 200
Plant Y / $10 / $5 / $6 / 175
Plant Z / $12 / $7 / $8 / 75
Warehouse demand / 250 / 100 / 150 / 500 \ 450

a)Set up this transportation problem by adding a dummy plant. Then use the northwest-corner rule to find an initial basic feasible solution.

b)What is the optimal solution?

C.22 Jim Lloyd, vice president for operations of HHN, Inc., a manufacturer of cabinets for telephone switches, is constrained from meeting his 5-year forecast by limited capacity at the company’s three existing plants. These plants are Waterloo, Pusan, and Bogota. As his able assistant, you have been told that because of existing capacity constraints and the expanding world market for HHN cabinets, a fourth plant is to be added. The real estate department has advised Lloyd that two sites seem particularly good because of stable political situations and tolerable exchange rates. These two locations are Dublin, Ireland, and Fontainebleau, France. Lloyd suggests that from the data in the following table, which provide production and transportation costs, you should be able to determine where the fourth plant should be located. (Note: This problem is degenerate with the data for both locations.)

Plant Location

Market AreaWaterlooPusanBogotaFontainebleauDublin

Canada: Demand 4,000

Production cost5030405045

Transportation cost1025202525

South America: Demand 5,000

Production cost5030405045

Transportation cost2025103030

Pacific Rim: Demand 10,000

Production cost5030405045

Transportation cost2510254040

Europe: Demand 5,000

Production cost5030405045

Transportation cost2540301020

Capacity8,0002,0005,0009,0009,000

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