More Complex Feasible Regions

The situations we have looked at so far have only one constraint (as well as the usual non-negativity constraints). Most real world situations have more constraints than this.

With our fertilizer example, how does the situation change if (a) the farmer has already committed himself to buy two bags per hectare of the high-grade fertilizer, and (b) he only has enough total storage space for a total of nine bags per hectare. Now we are working with three constraints. What does this do to the feasible region? This page requires a Java capable browser.

The two new constraints can be expressed as:

Use the applet to demonstrate how each constraint reduces the feasible region.

What are the coordinates of the vertices that define the limits of the feasible region? Drag the red dot to each corner of the feasible region and record it's coordinates.

Exercise 5.

Use the applet to determine the coordinates of the vertices that define the limits of the feasible region for the following sets of constraints. (You may also assume non-negativity constraints for x and y.)

(Each of these has three constraints: two less than or equal to, and one greater than or equal to. There's nothing special about these combinations of constraints, it's just that this is what the applet is set up for. You could equally well have, say, seven constraints, all less than or equal to. You could also have several greater than or equal to constraints, although this kind of constraint is less common in real situations.)

a)

b)

c)

Check your answers