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

In an LP problem, to evaluate the basic variables in Simplex method, which of the following method is used?

• A) Gauss Elimination method
• B) Gauss-Seidel method
• C) Gauss Least Square method
• D) Gauss-Jordan method

Shortcoming of Big M method is that the value of M could be ____________.

• A) negative
• B) very large
• C) positive
• D) very small

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

• A) non-basic feasible
• B) basic feasible
• C) optimal
• D) degenerate

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) one slack
• C) three objective
• D) two artificial

Big M technique is used if the initial basic solution obtained using slack variables is _______.

• A) inconsistent
• B) feasible
• C) optimal
• D) infeasible

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;(2,4,1,2), then it is ---------- solution.

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

While solving an LP problem by Simplex method, the inclusion of slacks in the constraints’ inequalities helps in finding ------------- variables.

• A) artificial
• B) non-basic
• C) basic
• D) decision

In a feasible region, if the end points of the line segment are basic solutions, then all the points between these two will ------------.

• A) be non basic
• B) be optimal
• C) also be the basic
• D) be infeasible