Operation Research :- Question bank
UNIT-I
Linear Programming
Q.1.
Explain the properties of Liner Programming. [4]
Q.2. Answer the questions related to the model
below: [4]
max.
3 x1 + 2 x2
st
2 x1 + 2 x2 ≤ 5
2
x1 + x2 ≤ 4
x1
+ 2 x2 ≤ 4
x1,
x2 ≥ 0
a.
Use the graphical solution technique to find the optimal solution to the model.
b. Use the simplex algorithm to find the optimal
solution to the model.
c. For which objective function coefficient value
ranges of x1 and x2 does the solution remain optimal? d. Find the dual of the
model.
Q.3. what is the
allowable range for the objective function coefficient of x2 in which current
solution (basis) remains optimal? (Hint: Use the relation of
Duality-Sensitivity)
Q.4. Explain
maximization and minimization models with example. [4]
Q.5. Explain
mathematical model of single period production model. [4]
UNIT-II
Duality
in Linear Programming
Q.1.Explain
Primal dual relationship. [4]
a)
Weak Duality Property
b)
Optimality Property
Q.2. Explain the Steps involved in the dual simplex
method. [4]
Q.3. Write down the steps for solving Revised
Simplex Method in Standard Form [4]
Q.4. What is the
principle of duality in linear programming? [4]
Q.5. What is an
economic interpretation of duality?
UNIT-III
The Transportation Problem and
Assignment Problem
Q.1. Consider the
following transportation table for a minimization problem. [4]
a) A basic feasible solution for the given
transportation is given as BV: {x11, x13, x21, x24, x32, x33}. Find the values
of the basic variables. Prove that this solution is not optimal.
b) Find the optimal solution using transportation
simplex method starting from the basic feasible solution given in part a.
c) Find the range of values of the c24 (the cost
related to x24ı) for which the current basis remains optimal.
[4]
Q.2. A
shoe company forecasts the following demands during the next three months: 200,
260, 240. It costs $7 to produce a pair of shoes with regular time labor (RT)
and $11 with overtime labor (OT). During each month regular production is
limited to 200 pairs of shoes, and overtime production is limited to 100 pairs.
It costs $1 per month to hold a pair of shoes in inventory. Formulate a
balanced transportation problem to minimize the total cost of meeting the next
three months of demand on time .
Q.3. Explain the following terms: [4]
a)
North West corner method,
b)
Least cost method,
Q.4. Write & Explain MODI method algorithm steps. [4]
Q.5.Define Stepping
Stone Method. [4]
UNIT-IV
Game
Theory and Dynamic Programming
Q.1. Discuss 2 person 0 sum games model in game theory.
Write payoff function of the same. [4]
Q.2. Solve the 2
x 2 game. Consider the following game and solve it using graphical
method.
 |
Q.3. Explain Forward and backward recursion. [4]
Q.4. Explain Dynamic Programming (DP) Applications [4]
a) Knapsack
b)
Equipment replacement
Q.5. Solve.
[4]
Knapsack Max weight : W = 10 (units)
Total items : N = 4
Values of items : v [] = {10, 40, 30, 50}
Weight of items :
w [] = {5, 4, 6, 3}
UNIT-V
Integer Programming Problem and Project
Management
Q.1. Explain in detail Integer Programming Method [4]
a) Binary Variables
b) Logical Constraints
Q.2. Explain Cutting Plane Algorithms with example. [4]
Q.3.
Discuss the rules for drawing network analysis with example. [4]
(Example 1For preparation of Paneer (Cottage Cheese))
Q.4. What
is CPM & PERT What are the objectives of CPM & PERT? [4]
Q.5. Explain in details
Scheduling and Crashing of Jobs. [4]
UNIT-VI
Decision Theory and Sensitivity Analysis
Q.1. Explain Decision Making Under Certainty Uncertainty
and Risk with Examples. [4]
Q.2. Solve- [4]
If
a firm having a contract to build a dam across a river requiring 300,000 cubic
meters of gravel, found two feasible sources whose characteristics are given
below:
Q.3. What is goal programming
distinguish it from linear programming? [4]
Comments
Post a Comment