Sample questions for LP: 1.
The maximization or minimization of a quantity is the a. goal of management science. b. decision for decision analysis. c. constraint of operations research. d. objective of linear programming.
2.
Decision variables a. tell how much or how many of something to produce, invest, purchase, hire, etc. b. represent the values of the constraints. c. measure the objective function. d. must exist for each constraint.
3.
Which of the following is a valid objective function for a linear programming problem? a. Max 5xy b. Min 4x + 3y + (2/3)z c. Max 5x2 + 6y2 d. Min (x1 + x2)/x3
4. Slack a. b. c. d.
is the difference between the left and right sides of a constraint. is the amount by which the left side of a < constraint is smaller than the right side. is the amount by which the left side of a > constraint is larger than the right side. exists for each variable in a linear programming problem.
6. The improvement in the value of the objective function per unit increase in a right-hand side is the a. sensitivity value. b. shadow price. c. constraint coefficient. d. slack value. 7.
Infeasibility means that the number of solutions to the linear programming models that satisfies all constraints is a. at least 1. b. 0. c. an infinite number. d. at least 2.
8. A constraint that does not affect the feasible region is a a. non-negativity constraint. b. redundant constraint. c. standard constraint. d. slack constraint. 9. All of the following statements about a redundant constraint are correct EXCEPT a. A redundant constraint does not affect the optimal solution. b. A redundant constraint does not affect the feasible region.
c. Recognizing a redundant constraint is easy with the graphical solution method. d. At the optimal solution, a redundant constraint will have zero slack. All linear programming problems have all of the following properties EXCEPT a. a linear objective function that is to be maximized or minimized. b. a set of linear constraints. c. alternative optimal solutions. d. variables that are all restricted to nonnegative values.
10.
1. What
is meant by 'Payoffs' in Game Theory?
A.Outcome of a game when different alternatives are adopted by players B.No. of players involved in a game
C.
value of a game
D.
strategies used by players
2. The A.
North West Corner rule
is used to find an initial feasible solution
B.is used to find an optimal solution C.is based on the concept of minimizing opportunity cost D.none of the given
The first step in formulating a linear programming problem is
1.
a. Identify any upper or lower bounds on the decision variables. b. State the constraints as linear combinations of the decision variables. c. Understand the problem. d. Identify the decision variables. e. State the objective function as a linear combination of the decision variables. 4.
The third step in formulating a linear programming problem is
a Identify any upper or lower bounds on the decision variables. b.State the constraints as linear combinations of the decision variables. c. Understand the problem. d.Identify the decision variables. e.State the objective function as a linear combination of the decision variables.
1: What is the objective function in linear programming problems? A constraint for available resource An objective for research and development of a company
A linear function in an optimization problem A set of non-negativity conditions
2: Which statement characterizes standard form of a linear programming problem? Constraints are given by inequilities of any type Constraints are given by a set of linear equations
Constraints are given only by inequalities of >= type Constraints are given only by inequalities of <= type
3: Maximize z = 2 x + 7 y subject to 3 x - 2 y <= 1 - x + 3 y >= -1 for non-negative x and y. Which of the following points are feasible: A(0,0), B(1,1), C(2,2)? A, B, and C A and B A and C B and C
4: Consider the constraint 5 x + 3 y - 4 z <= 7 Find the value of the slack variable s associated to this constraint for the point A(1,2,3). s = 8 s = 6 s = 0 s = -1
5: Maximize z = 3x for 0 <= x <= 5 . Find an optimal solution of the problem. x = 0 x = 1
x = 3 x = 5
11. Use this graph to answer the questions.
A
I
B
II
III
C D V IV
0
E
0
Max
20X + 10Y
s.t.
12X + 15Y < 180 15X + 10Y < 150 3X - 8Y < 0 X, Y > 0
a.
Which area (I, II, III, IV, or V) forms the feasible region?
b.
Which point (A, B, C, D, or E) is optimal?
c.
Which constraints are binding?
d.
Which slack variables are zero?
12. Maxwell Manufacturing makes two models of felt tip marking pens. Requirements for each lot of pens are given below.
Fliptop Model
Tiptop Model
Available
Plastic
3
4
36
Ink Assembly
5
4
40
Molding Time
5
2
30
The profit for either model is $1000 per lot.
a.
What is the linear programming model for this problem?
b.
Find the optimal solution.
c.
Will there be excess capacity in any resource?
13. Does the following linear programming problem exhibit infeasibility, or unboundedness? Explain.
Min
1X + 1Y
s.t.
5X + 3Y < 30 3X + 4Y > 36 Y < 7 X,Y > 0
14. For the following linear programming problem, determine the optimal solution by the graphical solution method. Are any of the constraints redundant? If yes, then identify the constraint that is redundant.
Max
X + 2Y
s.t.
X+ Y < 3 X 2Y > 0 Y < 1 X, Y 0
1. What is meant by 'Payoffs' in Game Theory? A.Outcome of a game when different alternatives are adopted by players B.No. of players involved in a game
C. value of a game D.strategies used by players
2. In Vogel's Approximation Method; the opportunity cost associated with a row is determined by A.the difference between the smallest cost and the next smallest cost in the row B.the difference between the smallest unused cost and the next smallest unused cost in the row C.the difference between the smallest cost and next smallest unused cost in the row D.none of the given
3. A competitive situation is known as a 'game' if it has given characterstics A.numbers of players is finite B.the players make individual decision without direct communication C.the payoff is fixed and determined in advance D.all given E.none of the given
4. In a departmental store customers arrive at a rate of 20 customers per hour. the average number of customers that can be handled by cashier is 24 per hour. What is service rate in this problem? A.20 B.3 C.24 D.10
5. Which of the following assertations is true of an optimal solution to an Linear Programming Problem? A.Every LP has an optimal solution B.The optimal solution always occur at extreme points C.If an optimal solution exists, there will always be atleast one at a corner D.All of the given
6. In a departmental store customers arrive at a rate of 20 customers per hour. the average number of customers that can be handled by cashier is 24 per hour. What is arrival rate in this problem? A.20 B.3 C.24 D.10
7. Which of the following is not a major requirement of a Linear Programming Problem? A.There must be alternative course of action among which to decide B.An objective for the firm must exist C.The problem must be of maximization type D.Resources must be limited
8. The North West Corner rule is used to find an initial feasible solution A.
B.is used to find an optimal solution C.is based on the concept of minimizing opportunity cost D.none of the given
9. The scientific method in O.R. study generally involves A.Judgement Phase B.Research Phase C.Action Phase D.All of the given E.None of the given
10. In a departmental store customers arrive at a rate of 20 customers per hour. the average number of customers that can be handled by cashier is 24 per hour. Probability that cashier is idle? A.1 B.1/6 C.5 D.5/6
Multiple choice questions based on Operation Research. Views (20551)
1. The first step in formulating a linear programming problem is a. Identify any upper or lower bounds on the decision variables. b. State the constraints as linear combinations of the decision variables. c. Understand the problem. d. Identify the decision variables. e. State the objective function as a linear combination of the decision variables. 2. The third step in formulating a linear programming problem is a Identify any upper or lower bounds on the decision variables. b.State the constraints as linear combinations of the decision variables. c. Understand the problem. d.Identify the decision variables.
e.State the objective function as a linear combination of the decision variables. 3. The following linear programming problem has been written to plan the production of two products. The company wants to maximize its profits. X1 = number of product 1 produced in each batch X2 = number of product 2 produced in each batch MAX: 150 X1 + 250 X2 Subject to:
2 X1 + 5 X2 ≤ 200
3 X1 + 7 X2 ≤175 X1, X2 ≥ 0 How much profit is earned per each unit of product 2 produced? a. 150 b.175 c. 200 d.250 4. A diet is being developed which must contain at least 100 mg of vitamin C. Two fruits are used in this diet. Bananas contain 30 mg of vitamin C and Apples contain 20 mg of vitamin C. The diet must contain at least 100 mg of vitamin C. Which of the following constraints reflects the relationship between Bananas, Apples and vitamin C? a. 20 A + 30 B ≥ 100 b.20 A + 30 B ≤100 c. 20 A + 30 B = 100 d.20 A = 100 5. The objective function for a LP model is 3 X1 + 2 X2. If X1 = 20 and X2 = 30, what is the value of the objective function? a. 0 b.50 c. 60 d.120 6. Why do we study the graphical method of solving LP problems? a. Lines are easy to draw on paper. b.To develop an understanding of the linear programming strategy. c. It is faster than computerized methods. d.It provides better solutions than computerized methods. 7. Level curves are used when solving LP models using the graphical method. To what part of the model do level curves relate? a. constraints b.boundaries c. right hand sides d.objective function 8. This graph shows the feasible region (defined by points ACDEF) and objective function level curve (BG) for a maximization problem. Which point corresponds to the optimal solution to the problem?
a.
A
b.
B
c.
C
d.
D
e.
E
