# Decision - Linear Programming Flashcards

1

Q

What are the steps in a linear programming question?

A

- Formulate the problem
- Plot constraints on a graph and identify feasible region
- Identify the maximum/minimum point (sliding rule/vertex testing)
- If an integer value is required, determine the integer value

2

Q

How do you formulate the problem in linear programming?

A

- State you decision variables (let x =, let y =)
- State your objective (minimise/ maximise P = x + y etc)
- State your constraints (including non-negativity constraint)

3

Q

How do you plot your constraints and identify the feasible region?

A

- Rearrange constraint for y to be subject and then plot the line (dotted/solid depending on inequality)
- Identify the feasible region (above/below line)

4

Q

How do you find the minimum/maximum point using the sliding ruler method?

A

- Rearrange the objective function for y to be the subject
- Plot the objective function with a random y-intercept
- Slide your ruler (with the same gradient as the line) up/down and find the first/last vertex of the feasible region it touches to find the minimum/maximum point
- Using simultaneous equations (equations of the constraint lines) find the minimum/maximum point
- Substitute values back into the objective function to find the value

5

Q

How do you find the minimum/maximum point using the vertex testing method?

A

- Using simultaneous equations (equations of the constraint lines) find the coordinates of every vertex of the feasible region
- Substitute values back into the objective function to find the value at each vertex
- Select the vertex which gives the largest/lowest value to be the maximum/minimum point

6

Q

What are the 2 methods to find the maximum/minimum point?

A

*Sliding ruler method

*Vertex testing method

7

Q

How would you find integer values for the maximum/minimum point when required?

A

- Find the coordinates of the optimal point
- Imagine a 1x1 box enclosing the optimal point with integer values as each corner of the box
- Test each point with each of the constraints (using a table) if they fail 1 of the constraints then do NOT consider that point any further.
- Out of the points which satisfy all the constraints, use the objective function to determine which has the maximum/minimum value for the integer value