Consider the following problem Max Z x1 st 5x1 x2 4 6x1 x3

Consider the following problem: Max Z = x1 s.t. 5x1 +x2 =4 6x1 + x3 =8 3x1 x4 = 3 xj GE 0 j Solve the problem by Inspection (do not use the Gauss-Jordan row operations), and justify your answer in terms of the basic solutions of the simplex method. Repeat (a) assuming that the objective function calls for minimizing z = x1.

Solution

from the given data i.e., on solving the subject to constraints, the values of X₁ are 4/5, 8/6 and 1 .

Hence the Maximum value of Z is 8 at the point (8/6,0)

the minimum value of Z is 3 at the point (1,0)