# 150+ Computer Aided Optimisation Techniques Solved MCQs

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1.

## Operations Research approach is _______.

A. multi-disciplinary
B. scientific
C. intuitive
D. collect essential data
2.

## Operation research approach is typically based on the use of _______.

A. physical model.
B. mathematical model.
C. iconic model.
D. descriptive model.
3.

## Mathematical model of linear programming problem 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 technique
Answer» A. it helps in converting the verbal description and numerical data into mathematical expression
4.

A. zero
B. 1
C. 5
D. 6
5.

A. 2
B. 3
C. finite
D. infinite
6.

## In a given system of m simultaneous linear equations in n unknowns (m<n) there will be ________.

A. n basic variables
B. m basic variables
C. (n-m) basic variables
D. (n+m) basic variables
7.

## A feasible solution to a linear programming problem _____.

A. must satisfy all the constraints of the problem 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
Answer» A. must satisfy all the constraints of the problem simultaneously
8.

## An Iso-profit line represents______.

A. an infinite number of solution all of which yield the same cost
B. an infinite number of solutions all of which yield the same profit
C. an infinite number of optimal solutions
D. a boundary of the feasible region
Answer» B. an infinite number of solutions all of which yield the same profit
9.

## While solving a linear programming problem in feasibility may be removed by _________.

C. removing a constraint
D. removing a variable
10.

## In the optimal simplex table, Zj-Cj=0 value indicates _____________.

A. alternative solution
B. bounded solution
C. infeasible solution
D. unbounded solution
11.

A. infeasible
B. unbounded
C. bounded
D. no solution
12.

## If all aij values in the entering variable column of the simplex table are negative, then _____.

A. there are multiple solutions
B. there exist no solution
C. solution is degenerate
D. solution is unbounded
13.

A. alternative
B. bounded
C. no solution
D. infeasible
14.

## For any primal problem and its dual______________.

A. optimal value of objective function is same
B. primal will have an optimal solution iff dual does too
C. both primal and dual cannot be infeasible
D. dual will have an optimal solution iff primal does too
Answer» B. primal will have an optimal solution iff dual does too
15.

## The right hand side constant of a constraint in a primal problem appears in the corresponding dual as___________.

A. a coefficient in the objective function
B. a right hand side constant of a function
C. an input output coefficient
D. a left hand side constraint coefficient variable
Answer» A. a coefficient in the objective function
16.

## Principle of complementary slackness states that____________.

A. primal slack*dual main=0.
B. primal main+dual slack=0
C. primal main+dual surplus=0
D. dual slack*primal main not equal to zero.
17.

## If primal linear programming problem has a finite solution, then dual linear programming problem should have____________.

A. finite solution
B. infinite solution
C. bounded solution
D. alternative solution
18.

## The initial solution of a transportation problem can be obtained by applying any known method. How-ever, the only condition is that__________.

A. the solution be optimal
B. the rim conditions are satisfied
C. the solution not be degenerate
D. the few allocations become negative
Answer» B. the rim conditions are satisfied
19.

## The dummy source or destination in a transportation problem is added to_______.

A. satisfy rim conditions
B. prevent solution from becoming degenerate
C. ensure that total cost does not exceed a limit
D. the solution not be degenerate
20.

## One disadvantage of using North-West Corner Rule to find initial solution to the transportation problem is that_______.

A. it is complicated to use
B. it does not take into account cost of transportation
C. it leads to a degenerate initial solution.
D. it does take into account cost of transportation.
Answer» B. it does not take into account cost of transportation
21.

## The calculations of opportunity cost in the MODI method is analogous to a_____.

A. Zj-Cj value for non-basic variable column in the simplex method.
B. value of a variable in XB-column of the simplex method.
C. variable in the B-column in the simplex method.
D. Zj-Cj value for basic variable column in the simplex method.
Answer» A. Zj-Cj value for non-basic variable column in the simplex method.
22.

## An unoccupied cell in the transportation method is analogous to a________.

A. Zj-Cj value in the simplex table.
B. variable in the B-column in the simplex table.
C. variable not in the B-column in the simplex table.
D. value in the XB column in the simplex table.
Answer» C. variable not in the B-column in the simplex table.
23.

## During iteration while moving from one solution to the next, degeneracy may occur when______________.

A. the closed path indicates a diagonal move
B. two or more occupied cells are on the closed path but neither of them represents a corner of the path.
C. two or more occupied cells on the closed path with minus sigh are tied for lowest circled value.
D. the closed path indicates a rectangle move.
Answer» C. two or more occupied cells on the closed path with minus sigh are tied for lowest circled value.
24.

## Which of the following methods is used to verify the optimality of the current solution of the transportation problem_________.

A. Modified Distribution Method
B. Least Cost Method
C. Vogels Approximation Method
D. North West Corner Rule
25.

## An optimal assignment requires that the maximum number of lines which can be drawn through squares with zero opportunity cost be equal to the number of______.

A. rows or coloumns
B. rows and coloumns.
C. rows+columns- 1
D. rows-columns.
26.

## While solving an assignment problem, an activity is assigned to a resource through a square with zero opportunity cost because the objective is to_________.

A. minimize total cost of assignment.
B. reduce the cost of assignment to zero
C. reduce the cost of that particular assignment to zero
D. reduce total cost of assignment
Answer» A. minimize total cost of assignment.
27.

## Maximization assignment problem is transformed into a minimization problem by_________.

A. adding each entry in a column from the maximum value in that column
B. subtracting each entry in a column from the maximum value in that column
C. subtracting each entry in the table from the maximum value in that table
D. adding each entry in the table from the maximum value in that table
Answer» C. subtracting each entry in the table from the maximum value in that table
28.

A. n!
B. (n+a)!
C. (n-a)!
D. n
29.

A. n
B. n-1
C. 2n-1
D. n-2
30.

A. 2n-1
B. n
C. n+1
D. n-2
31.

## A feasible solution to an LP problem______.

A. must satisfy all of the problems 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.
Answer» A. must satisfy all of the problems constraints simultaneously
32.

## An optimal solution to a maximization problem is reached if all

A. Zj-Cj>=0
B. Zj-Cj<=0
C. Zj-Cj=0
D. Zj-Cj is negative
33.

A. cells only
B. occupied
C. unoccupied
D. table
34.

## The solution must satisfy all the supply and demand constraints is called_____.

A. Feasible solution
B. Basic feasible solution
C. Initial basic feasible solution
D. rim conditions
35.

## Priority queue discipline may be classified as__________.

A. pre-emptive or non-pre-emptive
B. limited
C. unlimited
D. finite
36.

## The calling population is assumed to be infinite when______.

A. arrivals are independent of each other
B. capacity of the system is infinite
C. service rate is faster than arrival rate
D. all customers arrive at once
Answer» A. arrivals are independent of each other
37.

## Service mechanism in a queuing system is characterized by_____.

A. customers behavior
B. servers behavior
C. customers in the system
D. server in the system
38.

C. suddenly
39.

## Replace an item when________.

A. average annual cost for n years becomes equal to current running cost
B. next year running cost in more than average cost of nth year
C. present years running cost is less than the previous years average cost
D. average cost to date is equal to the current maintenance cost
Answer» A. average annual cost for n years becomes equal to current running cost
40.

## The average annual cost will be minimized by replacing a machine when_____.

A. average cost to date is equal to the current maintenance cost
B. average cost to date is greater than the current maintenance cost
C. average cost to date is less than the current maintenance cost.
D. next year running cost in more than average cost of nth year
Answer» A. average cost to date is equal to the current maintenance cost
41.

## The group replacement policy in suitable for identical low cost items which are likely to_________.

A. fail suddenly
B. fail completely and suddenly
C. fail over a period of time
D. progressive and retrogressive
Answer» C. fail over a period of time
42.

## The objective of network analysis is to___________.

A. minimize total project duration
B. minimize toal project cost
C. minimize production delays, interruption and conflicts
D. maximize total project duration
Answer» A. minimize total project duration
43.

A. forward pass
B. backward pass
C. critical
D. non critical
44.

## If an activity has zero slack, it implies that_________.

A. the project is progressing well
B. it is a dummy activity
C. it lies on the critical path
D. it lies a non critical path
Answer» C. it lies on the critical path
45.

## In program evaluation review technique network each activity time assume a beta distribution because_________.

A. it is a unimodal distribution that provides information regarding the uncertainty of time estimates of activities
B. it has got finite non-negative error
C. it need not be symmetrical about model value
D. the project is progressing well
Answer» A. it is a unimodal distribution that provides information regarding the uncertainty of time estimates of activities
46.

## Float analysis in useful for________.

A. projects behind the schedule only
B. projects ahead of the schedule only
C. cost at normal time is zero
D. the chain of activities may have a common event yet be independent by themselves
Answer» A. projects behind the schedule only
47.

## The activity which can be delayed without affecting the execution of the immediate succeeding activity is determined by_________.

A. total float
B. free float
C. independent float
D. variance of each float
48.

## In time cost trade off function analysis_________.

A. cost decreases linearly as time increases
B. cost increases linearly as time decreases
C. cost at normal time is zero
D. cost increases linearly as time increases
Answer» A. cost decreases linearly as time increases
49.

## A degenerate solution is one that ________.

A. gives an optimum solution to the Linear Programming Problem
B. gives zero value to one or more of the basic variables
C. yields more than one way to achieve the objective
D. makes use of all the available resources
Answer» B. gives zero value to one or more of the basic variables
50.

A. feasible
B. bounded
C. unbounded
D. infinite
51.

## When we solve a system of simultaneous linear equations by using two-phase method, the values of decision variables will be _______.

A. positive
B. negative
C. zero
D. positive and/or negative
52.

## The transportation problem deals with the transportation of ________.

A. a single product from a source to several destinations
B. a single product from several sources to several destinations
C. a single product from several sources to a destination
D. a multi -product from several sources to several destinations
Answer» A. a single product from a source to several destinations
53.

## The transportation problem is balanced, if _______.

A. total demand and total supply are equal and the number of sources equals the number of destinations.
B. none of the routes is prohibited
C. total demand equals total supply irrespective of the number of sources and destinations
D. number of sources matches with number of destinations
Answer» C. total demand equals total supply irrespective of the number of sources and destinations
54.

## The calling population is considered to be infinite when ________.

A. all customers arrive at once
B. capacity of the system is infinite
C. service rate is faster than arrival rate
D. arrivals are independent of each other
Answer» B. capacity of the system is infinite
55.

## The assignment problem is a special case of transportation problem in which ______.

A. number of origins are less than the number of destinations
B. number of origins are greater than the number of destinations
C. number of origins are greater than or equal to the number of destinations
D. number of origins equals the number of destinations
Answer» D. number of origins equals the number of destinations
56.

## Identify the correct statement

A. an assignment problem may require the introduction of both dummy row and dummy column
B. an assignment problem with m rows and n columns will involves a total of m x n possible assignments
C. an unbalanced assignment is one where the number of rows is more than, or less than the number of columns
D. balancing any unbalanced assignment problem involves adding one dummy row or column
Answer» C. an unbalanced assignment is one where the number of rows is more than, or less than the number of columns
57.

## The minimum number of lines covering all zeros in a reduced cost matrix of order n can be _____.

A. at the most n
B. at the least n
C. n-1
D. n+1
Answer» A. at the most n
58.

A. 5
B. 10
C. 15
D. 25
59.

## In marking assignments, which of the following should be preferred?

A. Only row having single zero
B. Only column having single zero
C. Only row/column having single zero
D. Column having more than one zero
Answer» C. Only row/column having single zero
60.

A. 6
B. 8
C. 12
D. 20
61.

## Customers arrive at a box office window, being manned ny single individual, according to Poisson input process with mean rate of 20 per hour, while the mean service time is 2 minutes. Which of the following is not true for this system?

A. E(n) = 2 customers
B. E(m) = 4/3 customers
C. E(v) = 6 minutes
D. E(w) = 16 minutes
Answer» A. E(n) = 2 customers
62.

A. 33%
B. 43%
C. 53%
D. 65%
63.

## The initial solution of a transportation problem can be obtained by applying any known method. However, the only condition is that____.

A. the solution be optimal
B. the rim conditions are satisfied
C. the solution not be degenerate
D. the solution be degenerate
Answer» B. the rim conditions are satisfied
64.

## An assignment problem can be solved by______.

A. Simplex Method
B. Transportation Method
C. Dual simplex method
D. Simplex and Transportation Method
Answer» D. Simplex and Transportation Method
65.

## A game is said to be fair if___

A. both upper and lower values of the game are same and zero
B. upper and lower values of the game are not equal
C. upper values is more than lower value of the game
D. lower values is more than upper value of the game
Answer» A. both upper and lower values of the game are same and zero
66.

## A mixed strategy game can be solved by ____.

A. Simplex Method
B. Dual Simplex Method
C. Transportation Method
D. Graphical Method
67.

## When the sum of gains of one player is equal to the sum of losses to another player in a game, this situation is known as_____.

A. two person game
B. zero-sum game
C. two person zero sum game
D. non zero sum game
68.

## The critical path satisfy the condition that _____.

A. Ei=Li and Ej=Lj
B. Ei-Li=Ej-Lj
C. Lj-Ei=Li-Ej
D. Lj+Ei=Li+Ej
69.

## In Program Evaluation Review Technique the maximum time that is required to perform the activity under extremely bad conditions is known as_____.

A. normal time
B. optimistic time
C. most likely time
D. pessimistic time
70.

## ._____is a mathematical technique used to solve the problem of allocating limited resource among the competing activities

A. Linear Programming problem
B. Assignment Problem
C. Replacement Problem
D. Non linear Programming Problem
71.

## The Hungarian method used for finding the solution of the assignment problem is also called ___________.

A. Vogel's Approximation Method
B. Modi Method
C. Simplex Method
D. Dual Simplex Method
72.

A. n!
B. n-1
C. (n-a)!.
D. n
73.

## In the production lot size model, increasing the rate of production _______ .

A. increase the optimal number of orders to place each year
B. does not influence the optimal number of orders
C. decrease the optimal number of orders to place each year
D. exactly the optimal number of orders to place each year.
Answer» A. increase the optimal number of orders to place each year
74.

A. normal
B. optimistic
C. pessimistic
D. most likely
75.

A. 2
B. 3
C. 4
D. 1
76.

A. critical time
B. normal time
C. cost slope
D. crash cost
77.

## The irreducible minimum duration of the project is called______.

A. critical time
B. crashed duration
C. cost slope
D. crash cost
78.

A. 1
B. 2
C. 3
D. 4
79.

A. slack
B. surplus
C. artificial
D. decision
80.

A. slack
B. surplus
C. artificial
D. decision
81.

## A feasible solution of an Linear Programming Problem that optimizes then the objective function is called _________

A. basic feasible solution
B. optimum solution
C. feasible solution
D. solution
82.

A. convex
B. polygon
C. triangle
D. bold
83.

A. zero
B. 1
C. 2
D. -1
84.

A. zero
B. 1
C. 2
D. -1
85.

## If all the constraints of the primal problem in equations are of type less than or equal to then the constraints in the dual problem is ___________.

A. less than or equal to
B. greater than or equal to
C. equal to
Answer» B. greater than or equal to
86.

## In an Linear Programming Problem functions to be maximized or minimized are called ___________.

A. constraints
B. objective function
C. basic solution
D. feasible solution
87.

## Linear Programming Problem that can be solved by graphical method has______.

A. linear constraints
C. non linear constraints
88.

## Charnes method of penalty is called __________

A. Simplex Method
B. Dual Simplex Method
C. Big-M Method
D. Graphical Method
89.

A. mn
B. m+n
C. m-n
D. m/n
90.

## Graphical method is also known as ___________.

A. Simplex Method
B. Dual Simplex Method
C. Big-M Method
D. Search Approach Method
91.

## The area bounded by all the given constraints is called _____________.

A. feasible region
B. basic solution
C. non feasible region
D. optimum basic feasible solution
92.

## If one or more variable vanish then a basic solution to the system is called ____________.

A. non feasible region
B. feasible region
C. degenerate solution
D. basic solution
93.

## The non basic variables are called ___________.

B. opportunity cost
C. slack variable
D. surplus variable
94.

A. symmetric
B. unsymmetric
C. square
D. non square
95.

A. symmetric
B. unsymmetric
C. slack
D. square
96.

A. dual-primal
B. primal-dual
C. dual
D. primal
97.

A. slack
B. surplus
C. artificial
D. pivot
98.

## ____________ method is an alternative method of solving a Linear Programming Problem involving artificial variables

A. Simplex Method
B. Big-M Method
C. Dual Simplex Method
D. Graphical Mehtod
99.

## The method used to solve Linear Programming Problem without use of the artificial variable is called __________.

A. Simplex Method
B. Big-M Method
C. Dual Simplex Method
D. Graphical Mehtod
100.

A. square
B. rectangle
C. triangle
D. polygon