Week 4 - Introduction To Linear Programming Formulation

Question 1

3 stages of Linear programming formulation

Answer 1

• Model development
• Optimise
• Sensitivity analysis

Question 2

What does model development consist of? (3)

Answer 2

• Identifying the decision variables
• Identify the objective function
• Identify all appropriate constraints
• Write the objective function and constraints as mathematical expressions

Question 3

What happens in the optimisation stage?

Answer 3

You systematically choose the values of the decision variables that make the objectives as large (for maximisation) or small (for minimisation) as possible and cause all of the constraints to be satisfied

Question 4

What is the importance of sensitivity analysis?

Answer 4

Is required to test effect of changes to input variables on the optimal solution

Question 5

What is a feasible solution? (2)

Answer 5

• Are any set of values of the decision variables that satisfies all the constraints
• The set of feasible solutions is called a feasible region

Question 6

Define infeasible solution (2)

Answer 6

• Is a solution that violates at least one constraint
• They are disallowed

Question 7

What is the desired feasible solution?

Answer 7

Is the one that provides the best value - minimum for a minimisation problem, maximisation for a maximisation problem for the objective (called the optimal solution)

Question 8

3 mains steps to answering a linear programming question

Answer 8

• Identify decision variables
• Identify objective function
• Identify the constraints

Question 9

How are constraints expressed? (3)

Answer 9

Expressed mathematically as algebraic inequalities or equations such as
• “<=“ which means “cannot exceed”
• “>=“ which means “at least”
• “=“ which means “must contain exactly”

Question 10

2 basic properties of a linear program

Answer 10

• The objective function and all constraints are linear functions of the decision variables - each function is a sum of terms each of which is some constant multiplied by a decision variable
• All variables are continuous - they may assume any real value

Question 11

Where is the feasible region on a constraint graph?

Answer 11

Below the fabrication and finishing constraint line and above the market mix constraint line

Question 12

How to get max profit?

Answer 12

Where the finishing and marketing mix constraint lines intersect or using a simultaneous equation

Question 13

Define unbounded solution (2)

Answer 13

• Occurs if the value of the objective can be increased or decreased without bound (I.e to infinity for a maximisation problem) without violating any of the constraints
• Generally indicates an incorrect model

Question 14

Define infeasibility

Answer 14

Is one for which no feasible solution exists - that it when there is no solution that satisfies all constraints together

Question 15

An example of when infeasibility can occur?

Answer 15

When a demand requirement is higher than available capacity or when managers from different departments have conflicting requirements or limitations