Linear Programming

1. The extreme point of the convex set of feasible solutions of the L.P.P. Max.Z = 10x₁ + 15x₂ S.t. x₁ + x₂ = 2,3x₁+2x₂ ≤ 6, x₁, x₂ ≥ 0 are

A) (2, 0), (0, 2)
B) (2, 0), (0, 3)
C) (0, 0), (0, 3)
D) (0, 2), (0, 3)

Answer is A) (2, 0), (0, 2)

2. If there is no feasible region in a L.P.P. then we are saying that the matter has

A) no solution
B) infinite solutions
C) unbounded solution
D) none of these

Answer is A) no solution

3. The solution of the L.P.P. Max. Z = 5x₁ + 7_x2 S.t. 3x₁ +2x₂≤ 12, 2x₁+3x₂≤13, x₁,x₂≥0 is

A) x₁=2, _x2 = 3, Z = 31
B) x₁ = 4, x₂ = 0, Z = 20
C) x₁= 0, x₂=13/3, Z = 91/3
D) none of these

Answer is A) x₁=2, x₂ = 3, Z = 31

4. The maximum number of basic solutions to the set of m simultaneous equations in n unknowns (n ≥ m) is

A) m
B) n-m
C) ⁿC_m
D) none of these

Answer is C) ⁿC_m

5. The set of values of the variable's x1,x2,.....xn, satisfy the constraints and non negative restrictions of a L.P.P. is called a :

A) no feasible solution
B) feasible solution
C) infinite solutions
D) none of these

Answer is B) feasible solution

6. If the worth of the target operate Z is accrued or small indefinitely, such solutions square measure called::

A) infinite solutions
B) no solution
C) unbounded solutions
D) none of these

Answer is C) unbounded solutions

7. A necessary and ample condition for the existence and non-degeneracy of all the essential solutions of Ax = b (m equations in n unknowns), is that each set of

A) linearly independent
B) linearly dependent
C) could or might not be linearly-independent
D) none of these

Answer is A) linearly independent

8. The non-negative variable's which are added to L.H.S. of the constraints to convert them into equalities square measure referred to as the::

A) surplus variables
B) slack variables
C) artificial variables
D) none of these

Answer is B) slack variables

9. A basic feasible solution of a L.P.P. is said to be non-degenerate basic feasible solution, if:

A) none of these basic variables is zero
B) at least one of the basic variables is zero
C) all of the basic variables are zero
D) none of these

Answer is A) none of these basic variables is zero

10. A basic feasible solution of a L.P.P. is said to be degenerate basic feasible solution, if:

A) none of the basic variables is zero
B) at least one of the basic variables is zero
C) all the basic variables are zero
D) none of these

Answer is B) at least one of the basic variables is zero