# Further Maths - Linear Programming

## Flashcards

### 2022-03-22

What are “decision variables”?

The variables in a linear programming problem that can be varied.

In a linear programming problem, what are $x, y$ and $z$ called?

The decision variables.

If you find suitable values for decision variables that fit the constraints, what have you found?

A feasible solution.

In a graphical linear programming problem, what is the area that contains all feasible solutions called?

The feasible region.

What is the optimal solution in a linear programming problem?

A feasible solution that meets the objective.

What are the three parts of formulating something as a linear programming problem?

- Define decision variables ($x$, $y$, etc.)
- State the objective and objective function (minimise $3x + …$)
- Stating the constraints as inequalities

How do you do solve a graphical linear programming problem?

Create an imaginary line with the gradient of the objective function and slide it to the first or last vertex in the feasible region.

What is the vertex testing method for linear programming?

Find the coordinates of each vertex in the feasible region and see which one gives the highest or lowest value for the objective function.

How do you deal with the fact the decision variables have to take on integer values in a linear programming problem?

Try out integer points near the optimal solution and see which one gives you the best value.

### 2022-05-03

When stating the final answers in a linear programming question, what is important?

State the values is the context of the problem (how many hours swimming?).

“Darren has enough dried fruit to make 3kg of $x$, 2kg of $y$ or $6kg$ of $z$”. How do you write this as an inequality?

What constraints do you normally forget to specify in a linear programming question?

The non-negativity constraints.