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QUESTION: 1

Simplex method of solving linear programming problem uses

Solution:

Simplex method of solving linear programming problem uses only the corner points of the feasible region.

QUESTION: 2

For the standard transportation linear programme with m sources and n destinations and total supply equaling total demand, an optimal solution (lowest cost) with the smallest number of non-zero xij values (amounts from source i to destinationj) is desired. The best upper bound for this number is:

Solution:

QUESTION: 3

Which one of the following is true in case of simplex method of linear programming?

Solution:

QUESTION: 4

The supply at three sources is 50, 40 and 60 units respectively whilst the demand at the four destinations is 20, 30, 10 and 50 units. In solving this transportation problem

Solution:

QUESTION: 5

Consider the Linear Programme (LP)

Maximize 4x + 6y

subject to 3x + 2y ≤ 6

2x + 3y ≤ 6

x, y ≥ 0

**Q. **

**After introducing slack variables s and t, the initial basic feasible solution is represented by the tableau below (basic variables are s = 6 and t = 6, and the objective function value is 0). **

After some simplex iteration, the following tableau is obtained

From this, one can conclude that

Solution:

As C_{j} = 0, 0 for x and y respectively therefore It is an optimal solution but not unique.

QUESTION: 6

Consider the Linear Programme (LP)

Maximize 4x + 6y

subject to 3x + 2y ≤ 6

2x + 3y ≤ 6

x, y ≥ 0

**Q. **

**The dual for the LP in Q 2 is: **

Solution:

Duplex method:

Step-I: Convert the problem to maximization form so Choice may be (b) or (c).

Step-II: Convert (≥) type con straints if any to (≤) type by multiplying such constraints by (–1) so our choice is (b).

QUESTION: 7

A company has two factories S1, S2 and two warehouses D1, D2. The supplies from S1 and S2 are 50 and 40 units respectively. Warehouse D1 requires a minimum of 20 units and a maximum of 40 units. Warehouse D2 requires a minimum of 20 units and, over and above, it can take as much as can be supplied. A balanced transportation problem is to be formulated for the above situation. The number of supply points, the number of demand points, and the total supply (or total demand) in the balanced transportation problem respectively are:

Solution:

QUESTION: 8

Which one of the following subroutines does a computer implementation of the simplex routine require?

Solution:

QUESTION: 9

A firm is required to procure three items (P, Q, and R). The prices quoted for these items (in Rs.) by suppliers S1, S2 and S3 are given in table. The management policy requires that each item has to be supplied by only one supplier and one supplier supply only one item. The minimum total cost (in Rs.) of procurement to the firm is:

Solution:

QUESTION: 10

In the solution of linear programming problems by Simplex method, for deciding the leaving variable

Solution:

QUESTION: 11

In order for a transportation matrix which has six rows and four columns, not to be degenerate, how much must be the number of allocated cells in the matrix?

Solution:

m + n - 1 = 4 + 6 - 1 = 9

QUESTION: 12

A tie for leaving variables in simplex procedure implies:

Solution:

QUESTION: 13

Consider the following statements:

The assignment problem is seen to be the special case of the transportation problem in which 1. m = n

2. All a_{i} = 1

3. x_{ij} = 1

(The symbols have usual meaning)

Which of the statements given above are correct?

Solution:

3 - is wrong

QUESTION: 14

Match List-I (Persons with whom the models are associated) with List-II (Models) and select the correct answer:

Solution:

QUESTION: 15

Which one of the following is not the solution method of transportation problems?

Solution:

Hungarian method is used in assignment problem (but remember assignment problem is a special case of transportation problem).

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