LINEAR PROGRAMMING PART 1

Question 1

A model consisting of linear relationships
representing a firm’s objective and resource
constraints

Answer 1

Linear Programming (LP)

Question 2

LP problem involves a linear objective
functions, which is the function that must be
maximized or minimized. This objective
function is subject to some constraints, which
are inequalities or equations that restrict the
values of the variables.

Answer 2

Linear Programming (LP)

Question 3

LP is used to find the best or optimal solution
to a problem that requires a decision about
how best to use a set of limited resources to
achieve

Answer 3

Linear Programming (LP)

Question 4

Determines the resource
capacity needed to meet demand over
an immediate horizon, including units produced, workers hired and

Answer 4

. Production Planning

Question 5

Menu of food items that meets nutritional or
other requirements, for example, hospital or school
cafeteria menus.

Answer 5

. Diet

Question 6

Assigns work to limited resources, example ; assigning jobs or workers to different
machines.

Answer 6

Assignment

Question 7

Mix of different products to
produce that will maximize profit or minimize cost
given resource constraints such as material, labor, budget, et

Answer 7

Production Mix

Question 8

Financial model that
determines amount to invest in different alternatives
given return objectives and constraints for risk, diversity, etc.

Answer 8

Investment Budgeting

Question 9

Schedules regular and
overtime production, plus inventory to carry over, to
meet demand in future periods.

Answer 9

Multi-period Scheduling

Question 10

Logistical flow of items (goods or
items) from sources to destinations.

Answer 10

Transportation

Question 11

Determines “recipe” requirement

Answer 11

Blend

Question 12

Maximizes the amount of flow from
sources to destinations; for example, the flow of work
in process through an assembly operation.

Answer 12

Maximal Flow

Question 13

Shortest routes from sources to
destinations.

Answer 13

Shortest Route

Question 14

Optimization in Medicine
The objective in an optimization model could be

Answer 14

 Maximize lifespan of a patient
 Maximize average lifespan of a population
 Minimize radiation exposure to healthy tissue
 Maximize radiation exposure to cancer tissue
 Minimize the probability of an adverse event
 Minimize costs

Question 15

Optimization in Medicine
The constraints in an optimization model could arise
due to:

Answer 15

 Budget constraints
 Maximum allowable exposure to a treatment
 Minimum or maximum time between treatments
 Maximum allowable risk level

Question 16

This system is generated when the
number of decision variables is equal to the number of
constraints, that is, the number of rows = the number
of columns. In this system, there exists a unique
solution.

Answer 16

Square system

Question 17

This system is generated when the
number of decision variables is lesser than the
number of constraints, that is, the number of
rows > the number of columns. In this system,
there are many representative solutions

Answer 17

Tall system

Question 18

This system is generated when the
number of decision variables is more than the
number of constraints, that is, the number of
ows < number of columns. In this system,
there is infinite solution.

Answer 18

Flat system

Question 19

Approaches used in Linear Programming

Answer 19

Geometric Approach, Algebraic Approach

Question 20

graphical method
- uses feasible region and corner points (coordinate
points)
to determine the optimal

Answer 20

Geometric Approach

Question 21

SIMPLEX method
developed by George B. Dantzig in 1947
- utilized if there are more decision variables and
problem constraints

Answer 21

Algebraic Approach

Question 22

APPLICATION FORMULATING LP MODELS STEP 1

Answer 22

Step 1. Read the problem carefully. If appropriate, organize the data into a table

Question 23

APPLICATION FORMULATING LP MODELS STEP 2

Answer 23

Step 2. Determine and define the variables. These
variables represent the unknown quantities whose
values are what you want to find.

Question 24

APPLICATION FORMULATING LP MODELS STEP 3

Answer 24

Step 3. Formulate the objective function. This is what
you want to maximize or minimize.

Question 25

APPLICATION FORMULATING LP MODELS STEP 4

Answer 25

Step 4. Formulate the constraints inequalities. These
are expressions that limit the amount of resources you
can use and the restrictions of your constraint
variables.

Question 26

APPLICATION FORMULATING LP MODELS STEP 5

Answer 26

Step 5. Solve the problem using an appropriate
algorithm or mathematical technique manually and/or
using any available

Question 27

A mathematical procedure for solving linear
programming problems; can handle two or more
decision variables.

Answer 27

Simplex Method

Question 28

A linear programming problem is

Answer 28

a. the objective function is to be maximized
b. all decision variables are nonnegative
C. all constraints involve <
d. the constants on the right side in the constraints are
all positive

Question 29

Simplex Method Step 1

Answer 29

Determine the objective function.

Question 30

Simplex Method Step 2

Answer 30

. Write down all necessary constraint

Question 31

Simplex Method Step 3

Answer 31

Convert each constraint into an equation by adding
a slack variable.

Question 32

Simplex Method Step 4

Answer 32

Set up the initial simplex table

Question 33

Simplex Method Step 5

Answer 33

Select pivot column by finding the most negative
indicator

Question 34

Simplex Method Step 6

Answer 34

6. Select pivot row. (Divide the last column by pivot
   column for each corresponding entries. Choose the
   smallest positive result. The corresponding row is
   the pivot row. In case there is no positive entry in
   pivot there is no optimal solutions. Stop!

Question 35

Simplex Method Step 7

Answer 35

7. Find pivot: Circle the pivot entry at the intersection
   of the pivot column and the pivot row, and identify
   entering variable and leaving variable . Divide pivot
   by itself in that row to obtain 1. Also obtain zeros for
   all rest entries in pivot column.

Question 36

Simplex Method Step 8

Answer 36

8. Perform row operation using Pivoting Method