The role of artificial variables in the 'Big M' technique is to _______________.

• A) optimize resource allocation
• B) maximize the objective function
• C) ensure feasibility of the initial basic solution
• D) minimize the objective function

In two phase method if the minimum value of objective function in the first phase is greater than zero, then the solution of original problem _____________.

• A) non of these
• B) exists
• C) is uncertain
• D) does not exists

While applying Simplex method to a LP of minimization type, we proceed stepwise from one basic feasible solution to another in such a way that the objective function always ---------- its value.

• A) increases
• B) oscillate
• C) does not change
• D) decreases

By which of the following method, any complex linear programming problem can be handled?

• A) Dual method
• B) Degenerate method
• C) Simplex method
• D) Graphical method

The solution set of the constraint: 2x+3y>12, will lie in --------- bisected by the line:2x+3y=12.

• A) both half planes
• B) opposite to the origin side in half plane
• C) first quadrant only
• D) origin side of half plane

While solving a Linear Programming problem by Simplex Method, an inequality constraint is transformed into strict equality by the inclusion of ---------- variable.

• A) basic
• B) decision
• C) slack
• D) artificial

The Simplex method is a-------------- for solving Linear Programming problem.

• A) computational procedure(Algorithm)
• B) graphical procedure
• C) probabilistic procedure
• D) analytical procedure

While solving a Linear Programming problem by Simplex method, we convert all the constraints'inequalities into------------.

• A) nothing but keep those strictly the same
• B) Equations with positive RHS
• C) opposite inequalities
• D) Equations with negative RHS

In linear programming, cycling occurs when the algorithm repeatedly follows the same sequence of iterations without converging to an optimal solution.

• A) True
• B) False
• C)
• D)

In Simplex method to solve an LP problem, Gauss Jordan Elimination method demands that all the key column entries should be zero except-----.

• A) 1st row entry
• B) last row entry
• C) row with maximum ratio on RHS column
• D) key row(pivot)entry

By Simplex method, to maximize ‘Z = 2x +9y’of an LP problem, if ‘z=0’ for the initial iteration then for its next improved solution, which of the following would be the next entering variable?

• A) x>0
• B) x<0
• C) y<0
• D) y>0

By Simplex method, to maximize ‘Z = 2x–9y’of an LP problem, if ‘z=0’ for the initial iteration then for its next improved solution, which of the following would be the next entering variable?

• A) x<0
• B) y<0
• C) x>0
• D) y>0

Solution region of the constraints: ‘2x+3y>12’ and ‘2x+3y<12’ will be the---------.

• A) straight line:2x+3y=12
• B) empty set
• C) point(6,4)
• D) all first quadrant

The solution set of the constraint: 2x+3y<12, will lie in --------- bisected by the line:2x+3y=12.

• A) first quadrant only
• B) opposite to the origin side in half plane
• C) origin side of half plane
• D) both half planes

When we have $\geq$ type constraints, then we convert it to equality constraints by introducing _______ variable(s) and solve it by __________ method.

• A) slack, Big M
• B) artificial and slack, Big M or Two phase
• C) artificial, Big M
• D) artificial, Two phase

$$Minimizing\,\,\,Z = 4{x_1} + 2{x_2} + {x_3}\,\,is\,\,equivalent\,\,to\,\,\max imizing\,\,Z = \_\_\_\_\_\_\_\_\_\_\_\_\_.$$

• A) $$- 4{x_1} - 2{x_2} - {x_3}$$
• B) $$- 4{x_1} + 2{x_2} + {x_3}$$
• C) $$- 4{x_1} - 2{x_2} + {x_3}$$
• D) $$- 4{x_1} + 2{x_2} - {x_3}$$

After converting constraints into the respective Standard equalities, we have an LP problem of ‘4’ equations in ‘6’ variables, then in a given iteration, how many Infeasible VARIABLES are possible to exists?

• A) 6
• B) 4
• C) 10
• D) 2

When ___________ fail to provide an initial basic feasible solution in the simplex method, we use the Big M Method.

• A) objective function
• B) artificial variables
• C) slack variables
• D) pivot variable

In Simplex standard table to solve an LP problem of Minimization, we choose the candidate for entering variable in-----------.

• A) Objective function with most negative coefficient
• B) Objective function with most positive coefficient
• C) Constraint with most positive coefficient
• D) Constraint with most negative coefficient

Once an LP problem is converted to a table, then calculation steps would be same for _____________ method(s).

• A) Big M
• B) Two phase
• C) simplex
• D) all of above