11C. Linear Programming

What is a linear programming problem? 1.A set of variables (in Further Maths there will only ever be two variables) called decision variables. 2.A set of restrictions or constraints on the value of these variables. 3.A function (called the objective function) of these two variables. We will want to either make this function as large as possible (maximise) or as small as possible (minimise).

There will only be two decision variables, so they can be graphed on x- and y- axes. The constraints are expressed as a set of inequations, like those in Ex 11B. The constraints are graphed and the solution region will be a polygon

The objective function The objective function is a function of the two decision variables usually related to cost, distance, or some other relationship. The maximum or minimum of the objective function occurs at one of the vertices (corner points) of the solution region polygon.

Worked examples Work through Worked Examples 6, 7, 8 on p Then try Ex 11C, Q.1, 2, 3

Follow Worked Example 9 on page 536, then try Ex 11C, Q. 5 Follow Worked Example 10 on page 538, then try Ex 11C, Q. 7 Finish with Ex 11C, Q. 8, 9, 10