4.3 The profit function

How much profit is made? Calling the profit P, it should be clear that

$$\fbox{$P = 1000 \,X + 1200\,Y$ ,}$$

so the problem is to find a point in the feasible region that maximizes profit.

To solve this maximization, we consider combination pairs of Type A and B networks that give equal profit; for example we could look at profit equal to 50000. For this profit level, then the (X,Y) pairs that give 50000 profit are found according to the equation:

$$\fbox{$50000 = 1000 \,X + 1200\,Y$ ,}$$

2 points on this line are (X = 50,Y = 0) and (X = 0, Y = 41 2/3).

If we plot this isoprofit line on the graph, we see that it looks possible to choose another (X,Y) pair that gives rise to a greater profit.

Other profit values for the isoprofit line can be tried: they are displayed here.

Notice:

As the profit increases the lines move out.

The lines are parallel (because they all have the same slope).

The best solution in this instance, will be given by the profit line that hits the top right hand corner of the feasible region.

This occurs where the 2 constraint lines cross (true in this example, but will not always be the case).