Find the maximum and minimum values of the given objective f

Find the maximum and minimum values of the given objective function of a linear programming problem. The figure below illustrates the graph of the feasible points. Objective function: z = 5x + 8y Use Gauss-Jordan elimination to solve the system below:

Solution

z(0,9) = 8*9=72

z(0,3) = 8*3 =24

z(3,0) = 5*3 =15 (min)

z(9,9) = 9*5+9*8 = 117 (max)

z(9,3) = 9*5+3*8 = 69