Question 1

The distinguishing feature of an LP model is
A)relationship among all variables is linear
B)it has single objective function & constraints
C)value of decision variables is non-negative
D)all of the above

Accepted Answer

A

Question 2

The best use of linear programming technique is to find an optimal use of
A)money
B)manpower
C)machine
D)all of the above

Accepted Answer

B

Question 3

Which of the following is not a characteristic of the LP
A)resources must be limited
B)only one objective function
C)parameters value remains constant during the planning period
D)the problem must be of minimization type

Accepted Answer

Linear Programming (LP) problems can be either of minimization or maximization type, not exclusively minimization. The other statements are characteristics of LP problems.

Question 4

Which of the following is an assumption of an LP model
A)divisibility
B)proportionality
C)additivity
D)all of the above

Accepted Answer

All of the options listed (divisibility, proportionality, and additivity) are assumptions of a linear programming (LP) model. These assumptions are fundamental for the mathematical formulation and solution of LP problems.

Question 5

Which of the following is a limitation associated with an LP model
A)the relationship among decision variables in linear
B)no guarantee to get integer valued solutions
C)no consideration of effect of time & uncertainty on lp model
D)all of the above

Accepted Answer

All of the options listed are limitations associated with Linear Programming (LP) models. LP assumes linearity in relationships, often does not guarantee integer solutions (unless it's an Integer Linear Program specifically), and typically does not account for time variability or uncertainty directly within the model framework.

Question 6

The graphical method of LP problem uses
A)objective function equation
B)constraint equations
C)linear equations
D)all of the above

Accepted Answer

The graphical method of Linear Programming (LP) problems uses the objective function equation to determine the level of optimization (maximization or minimization), constraint equations to define the feasible region, and linear equations since LP problems are composed of linear relationships.

Question 7

A feasible solution to an LP problem
A)must satisfy all of the problem's constraints simultaneously
B)need not satisfy all of the constraints, only some of them
C)must be a corner point of the feasible region
D)must optimize the value of the objective function

Accepted Answer

The answer of A feasible solution to an LP problem
A)must...

Question 8

An iso-profit line represents
A)an infinite number of solutions all of which yield the same profit
B)an infinite number of solution all of which yield the same cost
C)an infinite number of optimal solutions
D)a boundary of the feasible region

Accepted Answer

The answer of An iso-profit line represents
A)an infinite number of...

Question 9

If an iso-profit line yielding the optimal solution coincides with a constaint line, then
A)the solution is unbounded
B)the solution is infeasible
C)the constraint which coincides is redundant
D)none of the above

Accepted Answer

The answer of If an iso-profit line yielding the optimal...

Question 10

A constraint in an LP model becomes redundant because
A)two iso-profit line may be parallel to each other
B)the solution is unbounded
C)this constraint is not satisfied by the solution values
D)none of the above

Accepted Answer

A constraint in an LP model becomes redundant because two iso-profit lines may be parallel to each other.

Question 11

Constraints in LP problem are called active if they
A)represent optimal solution
B)at optimality do not consume all the available resources
C)both a & b
D)none of the above

Accepted Answer

Active constraints are those that are satisfied as equalities at the optimal solution, meaning they represent the optimal solution.

Question 12

Mathematical model of Linear Programming is important because
A)It helps in converting the verbal description and numerical data into mathematical expression
B)decision makers prefer to work with formal models.
C)it captures the relevant relationship among decision factors.
D)it enables the use of algebraic techniques.

Accepted Answer

A mathematical model of Linear Programming is important because it helps in converting the verbal description and numerical data into mathematical expressions, which is essential for solving optimization problems.

Question 13

In graphical method of linear programming problem if the iOS-cost line coincide with a side of region of basic feasible solutions we get
A)Unique optimum solution
B)unbounded optimum solution
C)no feasible solution
D)Infinite number of optimum solutions

Accepted Answer

When the iso-cost line coincides with a side of the region of basic feasible solutions in a linear programming problem, it means that every point on that line segment (which is part of the feasible region) represents an optimal solution. Therefore, there are infinitely many optimal solutions.

Question 14

If the value of the objective function can be increased or decreased indefinitely, such solution is called
A)Bounded solution
B)Unbounded solution
C)Solution
D)None of the above

Accepted Answer

An unbounded solution occurs when the value of the objective function can be increased or decreased indefinitely within the feasible region of a linear programming problem, indicating that there is no finite maximum or minimum value for the objective function.

Question 15

For the constraint of a linear optimizing function z=x1+x2 given by x1+x2?1, 3x1+x2?3 and x1, x2?0
A)There are two feasible regions
B)There are infinite feasible regions
C)There is no feasible region
D)None of these

Accepted Answer

The constraints x1 + x2 ≥ 1, 3x1 + x2 ≥ 3, and x1, x2 ≥ 0 do not overlap to form a feasible region in the first quadrant.

Question 16

If the number of available constraints is 3 and the number of parameters to be optimized is 4, then
A)The objective function can be optimized
B)The constraints are short in number
C)The solution is problem oriented
D)None of these

Accepted Answer

The number of constraints is less than the number of parameters to be optimized, indicating that there are not enough constraints to uniquely determine an optimal solution.

Question 17

Non-negativity condition is an important component of LP model because
A)Variables value should remain under the control of the decision-maker
B)Value of variables make sense & correspond to real-world problems
C)Variables are interrelated in terms of limited resources
D)None of the above

Accepted Answer

The non-negativity condition ensures that the values of variables in a Linear Programming (LP) model are realistic and applicable to real-world scenarios, where negative amounts of resources or outputs do not make sense.

Question 18

Maximization of objective function in an LP model means
A)Value occurs at allowable set of decisions
B)Highest value is chosen among allowable decisions
C)Neither of above
D)Both a & b

Accepted Answer

Maximization of an objective function in a linear programming (LP) model means selecting the highest value from the set of allowable decisions, which aligns with both statements A and B.

Question 19

Which of the following is not a characteristic of the LP model
A)Alternative courses of action
B)An objective function of maximization type
C)Limited amount of resources
D)Non-negativity condition on the value of decision variables.

Accepted Answer

The answer of Which of the following is not a...

Question 20

Which of the following statements is true with respect to the optimal solution of an LP problem
A)Every LP problem has an optimal solution
B)Optimal solution of an LP problem always occurs at an extreme point
C)At optimal solution all resources are completely used
D)If an optimal solution exists, there will always be at least one at a corner

Accepted Answer

The answer of Which of the following statements is true...

Quiz 6: Linear Programming LP Model and Techniques

The distinguishing feature of an LP model is

The best use of linear programming technique is to find an optimal use of

Which of the following is not a characteristic of the LP

Which of the following is an assumption of an LP model

Which of the following is a limitation associated with an LP model

The graphical method of LP problem uses

A feasible solution to an LP problem

An iso-profit line represents

If an iso-profit line yielding the optimal solution coincides with a constaint line, then

A constraint in an LP model becomes redundant because

Constraints in LP problem are called active if they

Mathematical model of Linear Programming is important because

In graphical method of linear programming problem if the iOS-cost line coincide with a side of region of basic feasible solutions we get

If the value of the objective function can be increased or decreased indefinitely, such solution is called

For the constraint of a linear optimizing function z=x1+x2 given by x1+x2?1, 3x1+x2?3 and x1, x2?0

If the number of available constraints is 3 and the number of parameters to be optimized is 4, then

Non-negativity condition is an important component of LP model because

Maximization of objective function in an LP model means

Which of the following is not a characteristic of the LP model

Which of the following statements is true with respect to the optimal solution of an LP problem