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

While solving a Linear Programming problem by Simplex Method, an inequality says:‘2x-3y<5’ is transformed into strict equality of the form---------, where ‘s>=0’.

• A) 2x-3y –s +A =5
• B) 2x-3y –s =5
• C) 2x-3y +s =5
• D) 2x-3y +s + A=5

The cost coefficient of artificial variable in Objective function is -------------.

• A) 0
• B) 1
• C) M
• D) > than 1

For $Z = 4 x_1 + x_2$ subject to $3 x_1 + 4 x_2 \geq 20, x_1 + 5 x_ 2 \geq 15$, we have ___________ variables.

• A) six
• B) three objective
• C) one artificial
• D) two slack

After converting constraints into the respective Standard equalities, we have an LP problem of ‘4’ equations in ‘6’ variables, if the initial basic feasible solution is say;(2,4,0,2), then it is ---------- solution.

• A) non-degenerate infeasible
• B) degenerate feasible
• C) non-degenerate feasible
• D) degenerate infeasible

In an LP problem, to evaluate the basic variables in Simplex method in any iteration, we would have to express Objective function in terms of ------------- variables.

• A) Artificial
• B) Basic
• C) Non-basic
• D) Slack

The purpose of phase 1 in the two phase method is to ________ .

• A) to maximize the objective function
• B) to introduce slack variables
• C) to minimize the sum of artificial variables
• D) to minimize the objective function

While solving an LP problem by Simplex method, if we have ‘3’ constraint equations in ‘5’ variables then to find basic variables we have to put any ------- variables equal to zero.

• A) 2
• B) 4
• C) 1
• D) 3

In graphical solution of solving Linear Programming problem to convert inequalities into
equations, we ----------------.

• A) use Artificial surplus variables
• B) use Slack variables
• C) use Surplus variables
• D) simply assume them to be equations

The straight line associated with the constraint;2x+3y<12,will meet x-axis at a distance of-------- units from origin.

• A) 3
• B) 6
• C) 2
• D) 4

Solution region of the constraints: 2x+3y>12 or 6x+9y=36, will be the half plane bisected by ‘2x+3y=12’, ----------- all the points on ‘2x+3y=12’.

• A) excluding
• B) including
• C)
• D)

The positive slack variables indicate -----------------.

• A) excess resource available
• B) nil resources
• C) shortage of resources
• D) idle(waste) resource

If in a LP problem, the objective is to maximize: z = 2x+3y, with all associated constraints of ‘=<’ type, then in the 1st iteration, z = ---------.

• A) 6
• B) 0
• C) 5
• D) 1