MMW

Question 1

What is Linear Programming?

Answer 1

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

Question 2

What does Linear Programming involves?

Answer 2

Linear objective functions. It must be maximized or minimized and subject to constraints which are inequalities or equations that restrict the values of the variables.

Question 3

What is Linear Programming used for?

Answer 3

It is 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 a goal or an objective.

Question 4

What are the real world applications of linear programming?

Answer 4

Production planning, diet, assignment, production mix, investment budgeting, multi-period scheduling, transportation, blend, maximal flow and shortest route

Question 5

What are its application in Medicine?

Answer 5

Maximize lifespan of a patient, population or
radiation exposure to cancer tissue.

Minimize radiation exposure to healthy tissues, probability of an adverse event or cost.

Question 6

The constraints in an optimization model are due to what?

Answer 6

Budget constraints, maximum allowable exposure to treatment, minimum or maximum time between treatments, maximum allowable risk level.

Question 7

Model of an objective function

Answer 7

z = c1x1 +c2x2 + … + CnXn

Question 8

Constraints model

Answer 8

a11x1 +a12x2 + … + a1nxn (<-=->)b1
a21x1 +a22x2 + … + a2nxn (<-=->)b2

am1x1 +am2x2 + … + amnxn (<-=->)bm

Question 9

What is a square system?

Answer 9

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.

Question 10

What is a tall system?

Answer 10

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 solution.

Question 11

What is the Flat system?

Answer 11

the number of decision variables is greater than the number of constraints, that is, the number of rows < number of columns. In this system, there is infinite solution.

Question 12

What are the approaches in Linear Programming?

Answer 12

1. Geometric Approach
   - graphical method
   - feasible region and corner points (coordinate points) to determine the optimal solution
2. Algebraic Approach
   -SIMPLEX method
   -developed by George B. Dantzig in 1947
   -utilized if there are more decision variables and problem constraints

Question 13

What is the 1st step in formulating Linear Programming Models?

Answer 13

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

Question 14

What is the 2nd step in formulating Linear Programming Models?

Answer 14

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

Question 15

What is the 3rd step in formulating Linear Programming Models?

Answer 15

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

Question 16

What is the 4th step in formulating Linear Programming Models?

Answer 16

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

Question 17

What is the 5th step in formulating Linear Programming Models?

Answer 17

Solve the problem using an appropriate algorithm or mathematical technique manually or through a software.

Question 18

What are Corner Points?

Answer 18

These points (vertices) are most likely carries the optimal solution to the Linear Programming problem.

Question 19

What is the Feasible Region?

Answer 19

The shaded area bounded by the lines.