Chapter 6 Linear Programming

Question 1

What is a decision variable?

Answer 1

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

Question 2

What is a objective function?

Answer 2

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

Question 3

What are the constraints?

Answer 3

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

Question 4

What is a feasible solution?

Answer 4

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

Question 5

What is a feasible region?

Answer 5

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

Question 6

Wha tis the optimal solution?
Explain further.

Answer 6

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

Question 7

What is commonly forgotten when doing linear programming?

Answer 7

Non negativity

Question 8

How do you formulate a linear programming problem?

Answer 8

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

Question 9

What is the custom when sketching the feasible region?

Answer 9

To shade everything but the feasible region

Question 10

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

Answer 10

Objective line method aka Ruler Method
Vertex checking method

Question 11

Explain the Objective line method?

Answer 11

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

Question 12

Where will the maximum optimal solution be found?

Answer 12

The far end of the region

Question 13

Where will the minimum optimal solution be?

Answer 13

The near end of the feasible region

Question 14

What do you need to remember about giving answers?

Answer 14

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

Question 15

Explain the vertex checking method

Answer 15

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

Question 16

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

Answer 16

The vertex checking method as the solutions could be decimals

Question 17

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

Answer 17

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

Question 18

Explain how to do hard constarisnts

Answer 18

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