ABSTRACT
Figure D.1 shows the feasible region and the optimum solution. Let z be the objective function z = 8x1 + 6x2. We want to maximize objective function z. We rewrite this function as x2 = − 43 + z6 . The slope of this function is − 43 , and it intersects the x2-axis at (0, z). If we move this function up along the x2-axis while keeping its slope, z increases. On the other hand, if we move it down along the x2-axis, z decreases. As shown in Figure D.1, the maximum value of z is determined by moving the objective function up along the x2-axis while retaining the slope, − 43 , under the condition that the function passes through the feasible region. We obtain the maximum value of z = 132, when x2 = − 43 + z6 passes through (x1, x2) = (12, 6). We can obtain the same solution by the simplex method.
