35 Questions
| Total Attempts: 22847

Questions and Answers

- 1.Mark the correct statement about integer programming problems (IPPs):
- A.
Pure IPPs are those problems in which all the variables are non-negative integers.

- B.
The 0-1 IPPs are those in which all variables are either 0 or all equal to 1.

- C.
Mixed IPPs are those where decision variables can take integer values only but the slack/surplus variables can take fractional values as well.

- D.
In real life, no variable can assume fractional values. Hence we should always use IPPs.

- 2.Consider the following problem: Max. Z = 28x
_{1}+ 32x_{2}, subject to 5x_{1}+ 3x_{2}≤ 23, 4x_{1}+ 7x_{2}≤ 33, and x_{1}≥ 0, x_{2}≥ 0. This problem is:- A.
A pure IPP.

- B.
A 0-1 IPP.

- C.
A mixed IPP.

- D.
Not an IPP.

- 3.Mark the correct statement:
- A.
A facility location problem can be formulated and solved as a 0-1 IPP.

- B.
Problems involving piece-wise linear functions can be modeled as mixed linear programming problems.

- C.
Solution to an IPP can be obtained by first solving the problem as an LPP then rounding off the fractional values.

- D.
If the optimal solution to an LPP has all integer values, it may or may not be an optimal integer solution.

- 4.Mark the wrong statement:
- A.
To solve an IPP using cutting plane algorithm, the integer requirements are dropped in the first instance to obtain LP relaxation.

- B.
A cut is formed by choosing a row in the optimal tableau that corresponds to a non-integer variable.

- C.
A constraint picked from the optimal tableau is: 0x1 + x2 + 1/2 S1 – 1/3 S2 = 7/2. With S3 being a slack variable introduced, the cut would be: -1/2 S1 – 2/3 S2 + S3 = -1/2

- D.
The optimal solution to LPP satisfies the cut that is introduced on the basis of it.

- 5.In cutting plane algorithm, each cut which is made involves the introduction of
- A.
An ‘=’ constraint

- B.
An artificial variable

- C.
A ‘≤’ constraint

- D.
A ‘≥’ constraint

- 6.Which of the following effects does the addition of a Gomory have? (i) adding a new variable to the tableau; (ii) elimination of non-integer solutions from the feasibility region; (iii) making the previous optimal solution infeasible by eliminating that part of the feasible region which contained that solution.
- A.
(i) only

- B.
(i) and (ii) only

- C.
(i) and (iii) only

- D.
All the above

- 7.Mark the incorrect statement about Branch and Bound method.
- A.
It is not a particular method and is used differently in different kinds of problems.

- B.
It is generally used in combinatorial problems.

- C.
It divides the feasible region into smaller parts by the process of branching.

- D.
It can be used for solving any kind of programming problem.

- 8.Mark the wrong statement:
- A.
Goal programming deals with problems with multiple goals.

- B.
Goal programming realizes that goals may be under-achieved, over-achieved, or met exactly.

- C.
The inequalities or equalities representing goal constraints are flexible.

- D.
The initial tableau of a goal programming problem should never have a variable in the basis which is an under-achievement variable.

- 9.Mark the wrong statement:
- A.
A travelling salesman problem can be solved using Branch and Bound method.

- B.
An assignment problem can be formulated as a 0-1 IPP and solved using Branch and Bound method.

- C.
The Branch and Bound method terminates when the upper and lower bounds become identical and the solution is that single value.

- D.
The Branch and Bound method can never reveal multiple optimal solutions to a problem, if they exist.

- 10.If two deviational variables, d
^{-}or d^{+}for over-achievement, are introduced in a goal constraint, then which of the following would not hold:- A.
Each of them can be positive or zero.

- B.
Either d- or d+ is zero.

- C.
Both are non-zero.

- D.
Both are equal to zero.

- 11.Mark the wrong statement:
- A.
A ‘lower’ one-sided goal sets a lower limit that we do not want to fall under.

- B.
A two-sided goal sets a specific target missing which from either side is not desired.

- C.
In goal programming, an attempt is made to minimize deviations from targets.

- D.
In using goal programming, one has to specify clearly the relative importance of the various goals involved by assigning weights to them.

- 12.Mark the wrong statement:
- A.
Goal programming assumes that the decision-maker has a linear utility function with respect to the objectives.

- B.
Deviations for various goals may be given penalty weights in accordance with the relative significance of the objectives.

- C.
The penalty weights measure the marginal rate of substitution between the objectives.

- D.
A goal programming problem cannot have multiple optimal solutions.

- 13.Mark the wrong statement:
- A.
In goal programming, the goals are ranked from the least important (goal 1) to the most important (goal n), with objective function co-efficients Pi.

- B.
Existence of (multiple ∆j rows) Net Evaluation containing priority terms indicate a prioritized goal-programming problem.

- C.
A lower priority is never sought to be achieved at the expense of higher-priority goal.

- D.
The co-efficients, Pi’s are not assigned any actual values.

- 14.Which of the following is not an essential condition in a situation for linear programming to be useful?
- A.
An explicit objective function

- B.
Uncertainty

- C.
Linearity

- D.
Limited resources

- E.
Divisibility

- 15.There are other related mathematical programming techniques that can be used instead of linear programming if the problem has a unique characteristic. If the problem has multiple objectives we should use which of the following methodologies?
- A.
Goal programming

- B.
Orthogonal programming

- C.
Integer programming

- D.
Multiplex programming

- E.
Dynamic programming

- 16.There are other related mathematical programming techniques that can be used instead of linear programming if the problem has a unique characteristic. If the problem prevents divisibility of products or resources we should use which of the following methodologies?
- A.
Goal programming

- B.
Primary programming

- C.
Integer programming

- D.
Unit programming

- E.
Dynamic programming

- 17.Types of integer programming models are _____________.
- A.
Total

- B.
0 - 1

- C.
Mixed

- D.
All of the above

- 18.Which of the following is not an integer linear programming problem?
- A.
Pure integer

- B.
Mixed integer

- C.
0-1integer

- D.
Continuous

- 19.Which of the following is
*not*a requirement for a goal programming problem?- A.
Prioritization of goals

- B.
A single objective function

- C.
Linear constraints

- D.
Linear objective function

- E.
None of the above

- 20.If we wish to develop a stock portfolio wherein we maximize return and minimize risk, we would have to use
- A.
Pure integer programming

- B.
Goal programming

- C.
Zero-one integer programming

- D.
Mixed-integer programming

- E.
Nonlinear programming

- 21.Solving an integer programming problem by rounding off answers obtained by solving it as a linear programming problem (using simplex), we find that
- A.
The values of decision variables obtained by rounding off are always very close to the optimal values.

- B.
The value of the objective function for a maximization problem will likely be less than that for the simplex solution.

- C.
The value of the objective function for a minimization problem will likely be less than that for the simplex solution.

- D.
All constraints are satisfied exactly.

- E.
None of the above.

- 22.When using the branch and bound method in integer programming maximization problem, the stopping rule for branching is to continue until
- A.
The objective function is zero.

- B.
The new upper bound exceeds the lower bound.

- C.
The new upper bound is less than or equal to the lower bound or no further branching is possible.

- D.
The lower bound reaches zero.

- E.
None of the above

- 23.A goal programming problem had two goals (with no priorities assigned). Goal number 1 was to achieve a cost of $3,600 and goal number 2 was to have no wasted material. The optimal solution to this problem resulted in a cost of $3,900 and no wasted material. What was the value for the objective function for this goal programming problem?
- A.
300

- B.
-300

- C.
3300

- D.
0

- E.
None of the above

- 24.Which of the following is not a type of integer programming problem?
- A.
Pure integer programming problem

- B.
Blending problem

- C.
Zero-one programming problem

- D.
Mixed-integer programming problem

- 25.Potential problems with the cutting plane method include
- A.
It may never converge to a solution.

- B.
It can be used only for problems with two dimensions.

- C.
It may take a great deal of computer time to find a solution.

- D.
It does not produce a good integer solution until the final solution is reached.

- E.
Both c and d

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