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
x1 = number of units of variety A produced
x2 = number of units of variety B produced
then the constraints are:
x1 + 2x2 <= 10 (production time)
2x1 + x2 <= 10 (space)
x1 <= 4 (demand)
where
x1, x2 >= 0
and the objective is
maximise 2x1 + 3x2
It is plain from the diagram below that the maximum occurs at the intersection of
x1 + 2x2 = 10 and
2x1 + x2 = 10
Solving simultaneously, rather than by reading values off the graph, we have that x1=x2=(10/3) with the value of the objective function being (50/3).