Make two separate plots of the function f x 3x4 10x2 3 a P

Make two separate plots of the function f (x) = 3x4 10x2 3 . a) Plot for -4 x 3 b) Plot for -4 x 4 by matlab

Solution

use this example solve the problem below

Consider the objective function that we used to illustrate the optimality criterion, z = 3x3 x4 + 20

For any value of z, say z = 17, the objective function is represented by a straight line . As z increases to 20, the line corresponding to the objective function moves parallel to itself across the feasible region. At z = 20, it meets the feasible region only at the point x3 = x4 = 0; and, for z > 20, it no longer touches the feasible region. Consequently, z = 20 is optimal. The unboundedness criterion was illustrated with the objective function: z = 3x3 x4 + 20

Increasing x3 while holding x4 = 0 corresponds to moving outward from the origin (i.e., the point x3 = x4 = 0) along the x3-axis. As we move along the axis, we never meet either constraint (1) or (2). Also, as we move along the x3-axis, the value of the objective function is increasing to +. The improvement criterion was illustrated with the objective function

z = 3x3 + x4 + 20

Starting from x3 = 0, x4 = 0, and increasing x4 corresponds to moving from the origin along the x4-axis. In this case, however, we encounter constraint (2) at x4 = t = 1 and constraint (3) atx4 = t = 2. Consequently, to maintain feasibility in accordance with the ratio test, we move to the intersection of the x4-axis and constraint (2), which is the optimal solution