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QUESTION: 1

Consider the following linear programming problem:

Max. Z = 2A + 3B, subject to A + B < 10, 4A + 6B < 30, 2A + B < 17, A, B ≥ 0.

What can one say about the solution?

Solution:
When one of the constraint is parallel to objective function i.e., if slopes are equal then the LPP may contain multiple optimal solutions.

QUESTION: 2

The solution for the LPP is

Max z = 3x_{1} + 2x_{2}

s/t: 2x_{1} + 3x_{2} ≤ 30

3x_{1} + 2x_{2} ≤ 24

x1 + x_{2} ≥ 3

x_{1} , x_{2} ≥ 0

Solution:

Given,

2x_{1} + 3x_{2} ≤ 30 (0,10)(15, 0)

3x_{1} + 2x_{2} ≤ 24 (0, 12)(8, 0)

x_{1} + x_{2} ≥ 3 (0, 3)(3, 0)

z = 3x1 + 2x2

z(_{3,0}) = 9

z(_{0,3}) = 6

z(_{0,10}) = 20

z(_{2.4,8.4}) = 24

z(_{8,0}) = 24

QUESTION: 3

For a given LPP, Z = 50x1 + 25x2 (max) s/t: 2x1 + 3x2 ≤ 12

x1 , x2 ≥ 0

The type of solution obtained is

Solution:

Constraints:

2x_{1} + 3x_{2} ≤ 12 (0, 4)(6, 0)

x_{1} ≤ 4 (x_{1} = 4)

z(0,0) = 0

z(4,0) = 200

QUESTION: 4

A company produces two products P_{1} and P_{2} . The profits per unit of P_{1} and P_{2} are Rs.75 and Rs.36 respectively. The market share of the company is 50,000 units of P_{1} and 80,000 units of P_{2} .The product P_{1} require one unit of resource R_{1} and P_{2} requires 3 units of resource R_{1} . The company has a maximum of 60,000 units of R_{1} . The constraint for resource R_{1 }can be written as

Solution:

X_{1} + 3X_{2} ≤ 60, 000

QUESTION: 5

Min z = 4x_{1 }+ 6x_{2}

s/t: x_{1} + x_{2} ≤ 4

x_{1} + 2x_{2} ≥ 6

x_{1}, x_{2} ≥ 0

The type of solution is

Solution:

Given,

x_{1} + x_{2} ≤ 4; (0, 4)(4, 0)

x_{1} + 2x_{2} ≥ 6; (0, 3)(6, 0)

only one point:

Z(_{0,0}) = 0

Z(_{0,3}) = 18

Z(_{2,2}) = 20

Z(_{4,0}) = 16

QUESTION: 6

Which of the following type of solution is not possible in simplex method?

Solution:

Simplex method can handle only ≤ type constraints so infeasible solution is not possible.

QUESTION: 7

Which of the following statements are true?

I. Simplex method can handle only ≤ type constraints

II. Simplex method can be applied only when the number of decision variables are ≥ 3

III. Simplex method can be applied to only maximization problems

Solution:

QUESTION: 8

In a transportation problem rows are the supply points and columns are the demand points. If total supply is less than total demand then

Solution:

QUESTION: 9

Which one of the following statements is NOT correct?

Solution:

*Answer can only contain numeric values

QUESTION: 10

If the numbers of sources are 6 and the number of destinations are 7. The total number of non-redundant constraints in linear programming problem formulation is ___________

(A)12

(B)12

Solution:

m+n−1 = 6+7−1 = 12

*Answer can only contain numeric values

QUESTION: 11

Consider the given problem. Find the total cost of transportation using N-W method.

Solution:

TC = 20 × 5 + 25 × 4 + 5 × 8 + 4 × 40 + 8× 20 + 9 × 30

= 830

QUESTION: 12

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: 13

Match List-I (O.R. Techniques) with List-II (Application) and select the correct answer using the codes given below the lists:

Solution:

QUESTION: 14

In a 6 × 6 transportation problem, degeneracy would arise, if the number of filled slots were

Solution:

*Answer can only contain numeric values

QUESTION: 15

Determine the initial basic feasible solution of the following transportation problem by using VAM.

Solution:

TC = 13 × 11 + 6 × 17 + 3 × 18 + 4 × 20 + 7× 28 + 18 × 12 = 791

QUESTION: 16

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:

QUESTION: 17

In an assignment problem having n facilities and n jobs, what is the number of possible ways of making assignments?

Solution:

QUESTION: 18

If there are two constraints in an LPP of which one of the constraints is redundant. The maximum possible number of corner points of the feasible region is

As one constraint is redundant it will not touch feasible region.

Solution:

QUESTION: 19

Match the following

Solution:

QUESTION: 20

Consider the following statements regarding linear programming

1. Dual of a dual is the primal.

2. When two minimum ratios of the right hand side to the coefficient in the key column are equal, degeneracy may take place.

Select the correct answer from the codes given below

Codes:

Solution:

### Solution- Linear Programming Test-1

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