Class 8

Question 1

Define: Decision variable

Answer 1

amounts of either inputs or outputs

Question 2

Define: Objective function

Answer 2

mathematical statement of profit, cost, etc

Question 3

Define: Constraint

Answer 3

limitations that restrict the available alternative

Question 4

Define Parameter

Answer 4

give fixed model values for the set of feasible combinations of decision variables defined by the constraints

Question 5

Define Redundant constraint

Answer 5

a constraint that does not form a unique boundary of the feasible solution space. By defin

Question 6

Define: Binding constraint

Answer 6

a constraint that forms the optimal corner point of the feasible solution space. Not all of the constraints that define the feasible solution space will form the optimal corner point

Question 7

Define: slack

Answer 7

when the optimal values of decision variables are substituted into less than or equal to constraint and the resulting values is less than the right side value (less than constraint)

Question 8

Define: surplus

Answer 8

when the optimal values of decision variables are subtituted into a greater than or equal to constraint and the resulting value exceeds the right side value (greater than constraint)

Question 9

Define sensitivity analysis

Answer 9

a means for assessing the impact of potential changes to the numerical values of an LP Model

Question 10

Define range of optimality

Answer 10

the range of values for an objective funstion over which the solution values of the decision variables remain the same

Question 11

Define RHS value

Answer 11

changes in right hand values of constraints

Question 12

Define Shadow price

Answer 12

the amount by which the value of the objective function would change if there were a one-unit change in the RHS value of a constraint

Question 13

Define Range of feasibility

Answer 13

the range of values for the RHS of a constraint over which the shadow price remains the same

Question 14

List the 4 assumptions of linear programming

Answer 14

1) Linearity - impact of decision variables is linear in both the constraints and the objective function
2) Divisibility - non integer values of decision variables are acceptable
3) Certainty - values of parameters are known and constant
4) Non negativity - negatives values of decision variables are unacceptable

Question 15

8 steps in graphical solution methods for finding optimal solution to two variable problems

Answer 15

1) set up the objective function and constraints in a mathematical format
2) Plot the constraints
3) Identify the feasible solution space
4) Plot the objective function
5) Identify redundant constraints
6) Identify the solution and corner points
7) Minimization
8) Slack and surplus

Question 16

How do you plot a constraint (5 steps)

Answer 16

1) replace the inequality sign with and equal sign
2) determine where the line intersects each axis
3) Mark these intersections on the axes and connect them with a straight line
4) Indicate by shading whether the inequality is greater than or less than
5) repeat each step for each constraint

Question 17

How to plot the objective function (2 steps)

Answer 17

1) treat the objective function like an equation

2) Plot the line for the objective function just as you did with the constraints

Question 18

How to calculate optimal decision variables (2 steps)

Answer 18

1) convert to an equation with a single unknown

2) Simplify and substitute to calculate the second variable

Question 19

Calculation

Answer 19

answer in notes

Question 20

define feasible solution space

Answer 20

the set of all feasible combinations of decision as defined by the constraint