How do you graph linear programming problems?
Please see below.
In a linear programming problem, we have
- some conditions, which are expressed as inequalities. Their graphs are drawn to identify the feasible zone.
- Then we have an objective function , which needs to be maximized or minimized. For this we draw a line, which has same value, say
#x#, of the objective function. On lines parallel to it, you will have equal values, but different from #x#.
Identifying a line parallel to objective function in the feasible zone, where we reach the maximum or minimum value (as desired). The points common on this line and in feasible zone is the solution.
Sometimes solution may be single (identified as a point on the graph) or a segment, all points on which are solution. The latter is known as degenerate solution.
Some examples are available at here.