Which of the following best describes the simplex method?

• A) An approach for solving integer programming problems.
• B) A method for solving quadratic programming problems.
• C) A deterministic algorithm for solving linear programming problems.
• D) A probabilistic algorithm for solving nonlinear programming problems.

While solving a LP by Simplex method, which of the following corresponds to corner points of the feasible region in Graphical method?

• A) basic feasible solution
• B) non-negative solutions
• C) non-basic feasible solution
• D) non-feasible solution

While solving an LP problem by the Simplex method, in the standard table, the element at the intersection of key column and key row is called ------------- element.

• A) Slack
• B) Entering
• C) Leaving
• D) Pivot

The variants of the simplex method cannot be identified through numerical examples.

• A) False
• B) True
• C)
• D)

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 Basic feasible VARIABLES are possible to exists?

• A) 2
• B) 4
• C) 10
• D) 6

Which method is also known as the Charnes method of penalty in the artificial variable technique?

• A) Penalty Method
• B) Big Method
• C) Two Phase Method
• D) Slack Variable Method

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

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

• A) 4
• B) 6
• C) 3
• D) 2

How can a minimization problem can be converted into maximization problem?

• A) By multiplying each coefficient in the objective function by-1
• B) By negating the constraints
• C) By introducing slack variables
• D) By including artificial variables

The inequality $3x - 2y \geq 14$ is equivalent to______.

• A) $3x - 2y < - 14$
• B) $- 3x + 2y > 14$
• C) $3x - 2y \leq 14$
• D) $- 3x + 2y \leq - 14$

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

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

If an artificial variable is not included while converting a constraint of type:’>=’ into equation, then we will have -------- solution.

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

If the point (t,6) lies in the feasible region associated with constraint:2x+3y<=12, then the maximum value of ‘t’ would be----------.

• A) -4
• B) -3
• C) -1
• D) 0

In the Simplex method to solve an LP problem of minimization, if at the end of iteration, every entry of objective function row is negative then the given problem -------------.

• A) has no solution
• B) has been minimized
• C) needs further improvement
• D) can not be optimized

To remove artificial variable(s) from the objective function, we have __________ method(s).

• A) simplex
• B) both b and c
• C) Two Phase
• D) Big M

In the Simplex method to solve an LP problem of maximization, if at the end of an iteration, there is a negative coefficient in the objective row then the given problem---------.

• A) has been maximized
• B) needs further improvement
• C) has no solution
• D) cant be optimized

$${\text{Minimizing}}\,\,{\text{any}}\,\,{\text{function}}\,f({x_1},{x_2},{x_3},......,{x_n})\,{\text{subject}}\,{\text{to}}\,{\text{the}}\,{\text{set}}\,{\text{of}}\,{\text{constraints}}\,\,{\text{is}}\,\,{\text{equivalent}}\,{\text{to}}\,{\text{maximizing _________ subject}}\,{\text{to}}\,{\text{the}}\,{\text{same}}\,{\text{set}}\,{\text{of}}\,{\text{constraints}}{\text{.}}$$

• A) $$f( - {x_1},{x_2},{x_3},......,{x_n})$$
• B) $$f({x_1}, - {x_2},{x_3},......,{x_n})$$
• C) $$- f({x_1},{x_2},{x_3},......,{x_n})$$
• D) $$f( - {x_1}, - {x_2}, - {x_3},......, - {x_n})$$

While applying Simplex method to a LP of maximization 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) oscillates
• C) decreases
• D) does not change

While solving a LP problem by Simplex method in a given iteration, the new basic variable is ---------- and the variable remove from the basis is called ---------.

• A) (feasible, infeasible)
• B) (infeasible, feasible)
• C) (leaving, entering)
• D) (entering, leaving)

If initial basic solution is -----------, while solving an LP problem then no further iteration can be performed.

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