ASSIGNMENT 6(Based on Transportation Problems and Assignment Problems)

Q.1. Find the cost of transportation of the following transportation problem by Matrix Minima method:

DESTINATIONS ai2 11 10 3 7 4

1 4 7 2 1 8

3 9 4 8 12 9

bj 3 3 4 5 6

ORI

GIN

S

(a) 64 (b) 83 (c) 44 (d) None of the above

Q.2. For the following transportation problem, obtain the cost by adopting the North-West-Corner method.

D1 D2 D3 aiO1 5 1 8 12

O2 2 4 0 14

O3 3 6 7 4

bj 9 10 11

(a) 104 (b) 126 (c) 86 (d) None of the above

Q.3. Obtain the optimal cost of transportation for the following problem using VAM:

W1 W2 W3 W4 aiF1 19 30 50 10 7

F2 70 30 40 60 9

F3 40 8 70 20 18

bj 5 8 7 14

1

(a) 779 (b) 743 (c) 688 (d) None of the above

Q.4. Identical products are produced in three factories and sent to four warehouses for delivery to thecustomers. The costs of transportation, the capacities of the factories and the demands of the warehousesare given in the following matrix :

WAREHOUSES

W1 W2 W3 W4 CAPACITIES

F1 3 8 7 4 30

F2 5 2 9 5 50

F3 4 3 6 2 18

DEMANDS 20 60 55 40

FACT

ORI

ES

Find the minimum cost of transportation.

(a) 520 (b) 490 (c) 515 (d) None of the above

Q.5. Find the unfulfilled demand of the warehouse in the previous problem.

(a) 10 (b) 20 (c) 15 (d) None of the above

Q.6. Is there any alternative optimal solution to the problem in Q.5.?

(a) Yes (b) No (c) Nothing can be said

Q.7. Find the transportation cost of the following balanced T.P. by row minima method.

DEMAND

D1 D2 D3 D4 D5 ai

O1 4 7 0 3 6 14

SUPPLY O2 1 2 -3 3 8 9

O3 3 -1 4 0 5 17

bj 8 3 8 13 8

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(a) 77 (b) 55 (c) 66 (d) None of the above

Q.8. Find out the optimal (minimum) assignment cost from the following cost matrix.

I II III IV

A 9 6 6 5

B 8 7 5 6

C 8 6 5 7

D 9 9 8 8

(a) 25 (b) 40 (c) 35 (d) None of the above

Q.9. Find the minimum cost solution for the 4×4 assignment problem whose cost coefficients are as givenbelow :

I II III IV

1 4 5 3 2

2 1 4 -2 3

3 4 2 1 -5

(a) -2 (b) -4 (c) -3 (d) None of the above

Q.10. Consider the problem of assigning four operators to four machines. The assignment costs in ru-pees are given here. Operator I cannot be assigned to machine III and operator 3 cannot be assigned tomachine IV. Find the optimal cost of assignment.

I II III IV

1 5 5 _ 2

2 7 4 2 3

3 9 3 5 _

4 7 2 6 7

3

(a) 12 (b) 14 (c) 13 (d) None of the above

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ANSWERS

Q.1. (b)

Q.2. (a)

Q.3. (b)

Q.4. (a)

Q.5. (c)

Q.6. (b)

Q.7. (c)

Q.8. (a)

Q.9. (c)

Q.10. (b)

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ASSIGNMENT 6.pdfASSIGNMENT 6 SOLUTION.pdfSolution of ASS 6.pdf