1,656 -450 1 Table 2. 17 gives a summary of the characteristics of the various basic solutions. TABLE 2.17 S.No. Basic Non-basic Values of the basic Talue of the Is the Is the Is the of the vantables variables variables grven by the objective solution solution solution basic constraint equations function feasible? non- feasible and solution (are all degenerate optimal? 20?) fare all basie variables > 0?) 1 $1.52 x + x = 450 2x + - 600 .. X-150. X - 300 1.650 Yes No 2 *1.31 X, $2 +3) = 450 2x - 600 ..X - 300, ,- 150 900 Yes Yes No 3 Xy, 2x + = 600 X; - 450.300 No No No 4 +-450 600 X = - 150 No No No 5 1. X= 450 x + 3 = 600 1.800 Yes Yes Yes .: 150 6 $ 450, 5600 0 Yes Yes No Out of these solutions, solutions in which all basic variables x, are 2 0 will be basic feasible; solutions in which all basic variables are > 0 will be non-degenerate basic feasible and the basic feasible solution that optimizes the objective function will be the optimal basic feasible solution. It may be seen that solutions 1, 2, 5 and 6 are basic feasible, they are also non-degenerate. Out of these, solution 5 gives the maximum value of the objective function Z and is therefore, the optimal solution Solutions 3 and 4 are infeasible and are to be discarded from consideration. Thus the optimal solution to the problem is x = 0, x, = 450: Zmax 1,800 EXAMPLE 2.15-2 Find all the basic solutions to the following problem: Maximize Z-x, + 3x, + 3x, subject to x, + 2x2 + 3x; -4. 2x, + 3x2 + 5x, - 7. f27 Also find which of the basic solutions are (1) basic feasible, (ii) non-degenerate basic feasible, and (iii) optimal basic feasible