Linear programming involves finding optimal solutions to problems subject to linear equality constraints.

For example, a company can make 150 nuts and 120 bolts, but there is only material for making 200 items.

Each nut yields a profit of $2 and each bolt yields $5.

To maximize its profit (P), the constraints of the problem can be expressed as

These equations can be graphed to find a polygon representing a feasible region whose vertices represent possible solutions to the problem.

The vertex that yields the maximum P is (x=80, y=120).

The maximum P is 2(80) + 5(120), or $760.