Define linear programming .

Linear programming, often shortened to LP , is a way of solving problems that involve working within a set of constraints and require a quantity to be maximised or minimised . Typical uses are in finance and manufacturing, such as maximising profit when raw materials and machine time are limited.

What has to be defined first when formulating a linear programming problem, and why?

The decision variables have to be defined first. Both the constraints and the objective function are written in terms of the decision variables, so neither can be written down until it is settled what those variables stand for.

Define a constraint in a linear programming problem.

A constraint is a restriction on the values the decision variables are allowed to take. Each constraint is written as an inequality in terms of the decision variables, such as a limit on the machine time available each day.

A LevelFurther MathsEdexcelDecision 1FlashcardsLinear programmingLinear Programming (LP) problems

Linear Programming (LP) problems (Edexcel A Level Further Maths: Decision 1): Flashcards

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FrontFormulating a Linear Programming Problem
Define linear programming.

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Define linear programming.
Linear programming, often shortened to LP, is a way of solving problems that involve working within a set of constraints and require a quantity to be maximised or minimised.
Typical uses are in finance and manufacturing, such as maximising profit when raw materials and machine time are limited.
Define decision variables in a linear programming problem.
The decision variables are the quantities in the problem that can be varied, usually written $x$ , $y$ and $z$ .
They are typically a 'number of things', such as the number of chairs and the number of tables a manufacturer makes each day.
What has to be defined first when formulating a linear programming problem, and why?
The decision variables have to be defined first.
Both the constraints and the objective function are written in terms of the decision variables, so neither can be written down until it is settled what those variables stand for.
Define the objective function of a linear programming problem.
The objective function is the quantity that has to be optimised, written as a function of the decision variables.
$P$ is usually used where a quantity such as profit is to be maximised, and $C$ where a quantity such as cost is to be minimised.
Define a constraint in a linear programming problem.
A constraint is a restriction on the values the decision variables are allowed to take.
Each constraint is written as an inequality in terms of the decision variables, such as a limit on the machine time available each day.
Varnish takes 3 hours to dry on a chair and 2 hours on a table, and four drying zones each provide 6 hours a day. Complete the constraint on the number of chairs, $x$ , and tables, $y$ :
$3 x + 2 y \leq______$
The completed constraint is:
$3 x + 2 y \leq 24$
The four drying zones together give $4 \times 6 = 24$ hours of drying time, which is the limit the chairs and tables must share.
True or False?
The non-negativity constraint should be included in a formulated linear programming problem even when the question does not mention it.
True.
Write $x, y \geq 0$ whether or not the question states it.
The decision variables almost always represent a number of things, so negative values would be meaningless and a formulation that allows them is incomplete.

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