OR-Notes are a series of introductory notes on topics that fall under the broad heading of the field of operations research (OR). They were originally used by me in an introductory OR course I give at Imperial College. They are now available for use by any students and teachers interested in OR subject to the following conditions.

A full list of the topics available in OR-Notes can be found here.

Let

x_{1} = number of units of variety A produced

x_{2} = number of units of variety B produced

then the constraints are:

x_{1} + 2x_{2} <= 10 (production time)

2x_{1} + x_{2} <= 10 (space)

x_{1} <= 4 (demand)

where

x_{1}, x_{2} >= 0

and the objective is

maximise 2x_{1} + 3x_{2}

It is plain from the diagram below that the maximum occurs at the intersection of

x_{1} + 2x_{2} = 10 and

2x_{1} + x_{2} = 10

Solving simultaneously, rather than by reading values off the graph,
we have that x_{1}=x_{2}=(10/3) with the value of the objective
function being (50/3).