Consider the standard-form LP min 2x1 + 3x2 + 5x3 s.t. 2x1 + 5x2 + 3x3 = 12 x1, x2, x3 Ú 0 with current interior point solution x132 = 12, 1, 12.

(a) Sketch the feasible space in a diagram like Figure 7.4

(a) and identify both the current solution and an optimal extreme point.

(b) Sketch the corresponding affine-scaled feasible space showing scaled equivalents of all points in part (a).

(c) Derive the associated affine-scaled standard form 7.10 .