J E Beasley

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.

Linear programming tutorial question

A company produces two varieties of a product. Variety A has a profit per unit of £2.00 and variety B has a profit per unit of £3.00. Demand for variety A is at most four units per day.

Production constraints are such that at most 10 hours can be worked per day. One unit of variety A takes one hour to produce but one unit of variety B takes two hours to produce.

Ten square metres of space is available to store one day's production and one unit of variety A requires two square metres whilst one unit of variety B requires one square metre.

Formulate the problem of deciding how much to produce per day as a linear program and solve it graphically.