# Integer And Goal Programming Quiz

35 Questions | Total Attempts: 15252  Settings  Let's test your knowledge about 'Ínteger Programming and Goal Programming' with the help of this quiz. Try answering all the questions and see how good you score. Try sharing this quiz with your friends and compare your scores with each other. All the Best!

• 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 = 28x1 + 32x2, subject to 5x1 + 3x2 ≤ 23, 4x1 + 7x2 ≤ 33, and x1 ≥ 0, x2 ≥ 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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