Multiple Choic 2 - Very good PDF

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1) A solution to a transportation problem that has less than m + n − 1 cells with positive allocations in the transportation tableau is a.an optimal solution. b.an initial feasible solution. c.a minimum-cost solution. d.a degenerate solution. 2) The optimal solution is found in an assignment matrix when the minimum number of straight lines needed to cover all the zeros equals a.(the number of agents) − 1. b.(the number of agents). c.(the number of agents) + 1. d.(the number of agents) + (the number of tasks). 3) The stepping-stone method requires that one or more artificially occupied cells with a flow of zero be created in the transportation tableau when the number of occupied cells is fewer than a.m + n − 2 b.m + n − 1 c.m + n d.m + n + 1 4)The per-unit change in the objective function associated with assigning flow to an unused arc in the transportation simplex method is called the a. net evaluation index. b. degenerate value. c.opportunity loss. d.simplex multiplier. 5)The difference between the transportation and assignment problems is that a.total supply must equal total demand in the transportation problem b.the number of origins must equal the number of destinations in the transportation problem c.each supply and demand value is 1 in the assignment problem d.there are many differences between the transportation and assignment problems 6) An example of a heuristic is the a.minimum-cost method. b.stepping-stone method. c.Hungarian method. d.MODI method. 7) Using the transportation simplex method, the optimal solution to the transportation problem has been found when a. there is a shipment in every cell. b. more than one stepping-stone path is available. c. there is a tie for outgoing cell. d. the net evaluation index for each unoccupied cell is ≥ 0.

8) Identifying the outgoing arc in Phase II of the transportation simplex method is performed using the a. minimum cost method. b.MODI method. c.stepping-stone method. d.matrix reduction method. 9)The MODI method is used to a. identify an outgoing arc.

b.identify an incoming arc. c.identify unoccupied cells. d.identify an initial feasible solution. 10)To use the transportation simplex method, a transportation problem that is unbalanced requires the use of a. artificial variables. b.one or more transshipment nodes. c.a dummy origin or destination. d.matrix reduction. 11)To use the Hungarian method, a profit-maximization assignment problem requires a. converting all profits to opportunity losses. b.a dummy agent or task. c.matrix expansion. d.finding the maximum number of lines to cover all the zeros in the reduced matrix. 12)To use the transportation simplex method, a. there can be no unacceptable routes. b.the initial feasible solution cannot be degenerate. c.a minimization objective function must be the case. d.total supply must equal total demand.

Subjective Short Answer 25. Develop the transportation tableau for this transportation problem.

Destinatio n Origin

A

B 5

Supply 6

1

100 4

2

2

200 3

6

3

150 9

4 Demand

7 50

250

2 5 0 26. Solve the following transportation problem using the transportation simplex method. State the minimum total shipping cost. Origin Suppl Destinatio Deman

y A B

n 500 400

Shipping costs are: Sour ce X A 2 B 9 ANSWERS

d X Y Z

300 300 300

Destination Y Z 3 5 12 10

Destination Origin

1

2 2

A

3 3

Supply 5

200

500 300 9

B Demand

12

100 300

10 300

300

400

300

Total shipping cost = $5,200.

27. Canning Transport is to move goods from three factories (origins) to three distribution centers (destinations). Information about the move is given below. Solve the problem using the transportation simplex method and compute the total shipping cost. Origin Suppl Destination Deman y d A 200 X 50 B 100 Y 125 C 150 Z 125 Shipping costs are:

Destination X Y Z 3 2 5 9 10 -5 6 4 (Source B cannot ship to destination Z)

Origin A B C

ANSWERS Destination Origin

X

Y 3

A

75

B

10 0

C

25

D

50

2

Supply 5

125 9

200 10

5

99 9

6

250

100

4 125

0

Deman d

Z

0

150 0 50

125

125

Total shipping cost = $2,000.

28. The following table shows the unit shipping cost between cities, the supply at each origin city, and the demand at each destination city. Solve this minimization problem using the transportation simplex method and compute the optimal total cost. Destination Origin Terre Indianapolis Ft. Wayne South Supply Haute Bend St. Louis 8 6 12 9 100 Evansville 5 5 10 8 100 Bloomingto 3 2 9 10 100 n Demand 150 60 45 45

ANSWERS Destination Origin

Terre Haute

Indianapolis 8

St. Louis

6 10

100

Bloomingto n

50

Demand

Supply 9

45

5

10

100 8 100

3

150

South Bend

12 45

5 Evansville

Ft. Wayne

2

9

10

50

100 60

45

45

Ship 10 from St. Louis to Indianapolis, 45 from St. Louis to Ft. Wayne, 45 from St. Louis to South Bend, 100 from Evansville to Terre Haute, 50 from Bloomington to Terre Haute, and 50 from Bloomington to Indianapolis. The total cost is 1755

Question 5 : Manufacturer has three plants P1 , P2 , P3 producing same products . From these plants , the product is transported to four warehouse W1 ,W2 ,W3 and W4 . Each plant has a limited capacity , and each warehouse has specific demand . Each plant transport to each warehouse , but transportation cost vary for different combinations

Transportation cost per unit W1

W2

W3

P1

5

2

1

12

650

P2

9

4

2

6

320

P3

4

11

4

5

580

580

700

100

420

Demand

W4

Supply

Required : Determine the quantity for each warehouse in order to minimize total transportation costs using vogel approximation Method ....