# Chapter 6 Linear Programming Flashcards

1
Q

What is a decision variable?

A

The decision variables are the number of each things that can be varied

2
Q

What is a objective function?

A

The objective functions are the equations that you are trying to maximise or minimise

3
Q

What are the constraints?

A

The constraints are the things that give rise to the objective functions
Each constraint will give rise to one inequality

4
Q

What is a feasible solution?

A

A feasible solution is a solution that satisfies all the decision variables

5
Q

What is a feasible region?

A

A feasible region is a region in which all the feasible solutions can be found

6
Q

Wha tis the optimal solution?
Explain further.

A

The optimal solution is the feasible solution that meets the objective
There could be more than one optimal solution

7
Q

What is commonly forgotten when doing linear programming?

A

Non negativity

8
Q

How do you formulate a linear programming problem?

A

1) Define the decision variables (x,y,z etc)
2) State the objective (maximise or minimise, together with the objective function)
3) Write the constraints as inequalities

9
Q

What is the custom when sketching the feasible region?

A

To shade everything but the feasible region

10
Q

What are the 2 methods called for locating the optimal points?

A

Objective line method aka Ruler Method
Vertex checking method

11
Q

Explain the Objective line method?

A

For the objective line method you need to sland your ruler such that its gradient is the same as the objective functions. Then you move it across the page until it intercepts the feasible region

12
Q

Where will the maximum optimal solution be found?

A

The far end of the region

13
Q

Where will the minimum optimal solution be?

A

The near end of the feasible region

14
Q

A

The answer needs to be in context of the question with the profit being stated

15
Q

Explain the vertex checking method

A

In this method you first find the co ordinates of all of the vertices. Then you evaluate the objective function at all of these points
Hen you select the vertex that gives the optimal solution

16
Q

Which is the superior method for locating the optimal point why?

A

The vertex checking method as the solutions could be decimals

17
Q

What can you do if you you need too find integer solutions?

A

Find the decimal values then test the 4 integer values around it then check the constraints and objective function to find the highest/lowest profit

18
Q

Explain how to do hard constarisnts

A

Do that variable is … of the whole eg 2/5(x+y+z) would be 40%