1. Question Pages
Part A
2 195
4 201
5 231
6 198
10 335
Part B
5(2nd part) 231
6 371(1st part),373-376(2nd part)
artificial variable
One type of variable introduced in a linear program model
in order to find an initial basic feasible solution; an artificial
variable is used for equality constraints and for greater-
than or equal inequality constraints.
Primal Dual Relationship
I describe the relationship between the pivot operations of the simplex method on the
Primal LP and the corresponding operations on the Dual LP. So given a sequence of
pivot operations on the Primal LP, these is a corresponding sequence of pivot
operations on the Dual LP. We assume we start with the Primal LP in standard form.
maximize ∑j=1 n cj xj subject to ∑j=1 n aij xj ≤ bi 0≤j≤n and 1≤i≤m xj ≥0
We shall assume the bi are greater than or equal to 0, so that the initial x can be taken
to be 0. The Dual LP can be written in the form
minimize ∑i=1 m bi yi subject to ∑j=1 m aij yi ≥ cj 0≤j≤n and 1≤i≤m yi ≥0
Now rewrite both the Primal and Dual in augmented form to turn the inequalities into
equalities.

2. maximize ∑j=1 n cj xj subject
to ∑j=1 n aij xj + wi = bi 0≤j≤n and 1≤i≤m xj ≥0 and wi ≥0
minimize ∑i=1 m bi yi subject to ∑j=1 m aij yi - zj = cj 0≤j≤n and 1≤i≤m yi ≥0
There is a fundamental relationship between the x* variables of the Primal and
the z* variables of the Dual. We'll refer to these variables as dual to one another.
There is a similar relationship between the variables yi of the Dual and the wi of the
Primal. Again, refer to the variables as dual to one another. We can indicate the
correspondence by a table.
P x1 .. xn w1 . wm D z1 .. zn y1 . ym
Assuming the bi are all nonnegative, we have a natural initial starting basic feasible
solution for the Primal. We indicate this by a new table with an additional two rows to
indicate which variables are basic (*) and which are non basic (no * ). We indicate
basic for both Primal and Dual.
**** P x1 .... xn w1 .. wm D z1 .... zn y1 .. ym ******
Note that the variables that are basic in the Primal correspond to variables that are
nonbasic in the Dual, and variables that are basic in the Dual correspond to variables
that are nonbasic in the Primal.
Now suppose we perform a pivot operation on the Primal. We get a new set of basic
and nonbasic variables. To perform the corresponding pivot operation on the Dual one
must select a pivot element such that this basic-nonbasic relationship between the
Primal variables and corresponding Dual variables continues to hold. Hence if at some
point during the simplex procedure one has a table with basic variable for the Primal
indicated by * then, after performing the corresponding pivot operation on the Dual,
the basic variables for the Dual must be those whose corresponding Primal variables
are nonbasic. This is indicated in the following table.
**** P x1 .... xn w1 .. wm D z1 .... zn y1 .. ym ******
If one performs the simplex algorithm on the Primal and performs the corresponding
pivot operation on the Dual ( as indicated above), then if the Primal becomes optimal,
the Dual will become feasible. The feasibility of the Dual will be indicated by
obtaining nonnegative values for the basic variables. Note that in the initial table
above for the Dual, the basic variables for the Dual, the z* are not feasible unless all of
the cj are nonpositive.

3. Buffer stock
Buffer stock refers to an amount of physical stock that a company keeps on hand
to protect against unexpected supply and demand variations. Choosing the right
amount of buffer stock can be a difficult balance between waste and shortfall. In
a wider context, buffer stock involves governments buying and selling
commodities to attempt to stabilize prices.
While a company can estimate the amount of stock it will need on hand at any
time, this can prove incorrect for both supply and demand reasons. On the
supply side, a company may face delays in getting raw materials, may suffer
machinery breakdowns or labor disputes, and may find the levels of mistakes
and breakages in production is bigger than expected. On the demand side, a
company may find a product becomes more popular overall, or that changes
among rival sellers mean more customers come to the company.
There are several reasons to keep buffer stock at as low a level as possible.
Having too much can increase storage costs or strain the limits of existing
storage capacity. With perishable goods, excess stock can lead to wastage.
WHAT DO YOU MEAN BY PURE STRATEGY
WHAT IS LOOPING IN OPERATION RESEARCH

4. Advantages of Operations Research (OR) in Decision Making
1. Effective Decisions
Operations Research (OR) helps the managers to take better and quicker decisions. It
increases the number of alternatives. It helps the managers to evaluate the risk and results
of all the alternative decisions. So, OR makes the decisions more effective.
2. Better Coordination
Operations Research (OR) helps to coordinate all the decisions of the organisation. It
coordinates all the decisions taken by the different levels of management and the various
departments of the organisation. For e.g. It coordinates the decisions taken by the
production department with the decisions taken by the marketing department.
3. Facilitates Control
Operations Research (OR) helps the manager to control his subordinates. It helps the
manager to decide which work is most important. The manager does the most important
work himself, and he delegates the less important work to his subordinates.
Operations Research (OR) helps a manager to fix standards for all the work. It helps him
to measure the performance of the subordinates. It helps the manager to find out and
correct the deviations (difference) in the performance. So, OR facilitates control.
4. Improves Productivity
Operations Research (OR) helps to improve the productivity of the organisation. It helps to
decide about the selection, location and size of the factories, warehouses, etc. It helps in
inventory control. It helps in production planning and control. It also helps in manpower

5. planning. OR is used in expansion, modernisation, installation of technology, etc. OR uses
many different mathematical and statistical techniques to improve productivity. Simulation
is used by many organisations to improve their productivity. That is, they try out many
production improvement techniques on a small scale. If these techniques are successful
then they are used on a large scale.