2 ways to describe a linear programming problem:

• standard/canonical form
• augmented form

Example Linear Programming Structuring

Linear Programming Problem

given:

• a toy company make 2 toys: x₁ and x₂
• these toys are made of 2 materials: A and B
• to make toy x₁, it needs 5 units of A and 2 units of B
• to make toy x₂, it needs 3 units of A and 3 units of B
• there is a maximum of 30 units of A
• there is a maximum of 20 units of B
• each toy x₁ can be sold for $10
• each toy x₂ can be sold for $7

what is the optimum product mix that maximizes the profit?

Standard/Canonical Form

Standard form is the usual and most intuitive form of describing a linear programming problem

more details Canonical Form

Equation Form

Block Matrix Form

TODO

Slack/Augmented Form

Linear programming problems can be converted into an augmented form in order to apply the common form of the simplex algorithm

more details Slack Form

Equation Form

Block Matrix Form