Linear programming

Question 1

What is optimization?

Answer 1

Finding the best solution/ stratergy.

Question 2

What is linear programming?

Answer 2

This is a tool for modeling and solving optimization problems.

Question 3

What are the typical LP applications?

Answer 3

1) Production planning: maximizes total production profit, and satisfies sales demand or limitations on production capacity.
2) Logistics: meeting customer demand and minimizing transport costs.
3) Marketing: meeting a fixed budget and maximizing advertising effectiveness.
4) Financial planning: meeting total investment amount, any restrictions of investing in the available alternatives as well as maximizing return on investment.

Question 4

What is the objective of the problem?

Answer 4

The quantity that we are trying to maximize or minimize.

Question 5

What are the constraints?

Answer 5

These limit the degree to which the objective function can be pursued.

Question 6

What are the three parts of LP models?

Answer 6

1) Seek to optimize an objective function.
2) By modifying a set of decision variables.
3) Subject to a set of constraints.

Question 7

What are the decision variables?

Answer 7

These are the types of quantities that the decision-makers would like to determine in order to find the best strategy for a business problem.

Question 8

Step 1 of formulating a LP model

Answer 8

Define the decision variables. In order to formulate mathematical equality and inequalities we define decision variables usually in terms of X and Y.

Question 9

Step 2 of the formulation of LP model

Answer 9

Define what the objective is using the decision variables.

Question 10

Step 3 of formulating a LP model

Answer 10

Determine the constraints in a mathematical formula.

Question 11

Where must we keep the decision variables?

Answer 11

Keep decision variables on the left-hand side of the equation.

Question 12

What is a constraint that is often forgotten?

Answer 12

The specification that values cannot be negative/ can be negative.

Question 13

What type of variables are decision variables?

Answer 13

They are continuous.

Question 14

What assumption do we make for linear programming?

Answer 14

We assume that problem parameters are known with certainty.

Question 15

Steps to use Excel solver.

Answer 15

1) Summarise data in a table.
2) Define cells to contain the value of decision variables.
3) Define cells to store the left hand side value of each constraint.
4) Calculate the left hand side of each constraint.
5) Calculate the value of the objective function.

Question 16

What is the graphical solution method?

Answer 16

This is used when a business optimization problem only has two decision variables. Uses plotted lines to solve LP problems.

Question 17

What is a feasible region?

Answer 17

The solution space. The area in which correct values may lie.

Question 18

Steps for the graphical solution method

Answer 18

1) Determine the solution space by plotting the constraints.
2) Find the optimal solution by searching through the feasible region.

Question 19

How to plot the objective function?

Answer 19

Select an arbitrary value for the optimal solution function and plot that on the graph. Any points below this line provide a lower value and any points above the line provide a higher value.

Question 20

What is another way to find the optimal solution?

Answer 20

The corner point method.

Question 21

What is a binding constraint?

Answer 21

Changing this constraint would lead to a change in the optimal solution.

Question 22

What is a slack constraint?

Answer 22

This still forms the feasible region but if changed does not have an impact on the optimal solution.

Question 23

Special cases of LP

Answer 23

1) Multiple Optimal Solution
2) Infeasible LP
3) Unbounded LP