THE ISO-PROFIT-LINE SOLUTION METHOD A second approach to graphically solving linear programming problems employs the iso-profit line. This technique is often more speedy than the corner-point method, for we do not have to evaluate the profit at every corner. Instead, we draw a series of parallel profit lines. Any point along a particular iso-profit line will have the same profit or value of the objective function. The highest profit line (or one farthest from the zero origin) which touches the feasible region pinpoints the optimal solution. Example 4 Maximize Z 2x1 x2 subject to the consta int s x1 2 x2 10 x1 x2 6 x1 x2 2 x1 2 x2 1 x1 , x2 0 Example 7 Minmize Z 3x1 2 x2 subject to the consta int s 5x1 x2 10 x 1 x2 6 x 1 4 x2 12 x1 , x2 0