Answer to Question #113189 in Operations Research for ardil

Question #113189
For the following LP problem, graph the region of feasible solution and solve by the corner-point method.

Maximize z = 5x1 + 8x2
Subject to x1 + x2 ≥ 6
3x1 + 2x2 ≤ 30
2x1 + x2 ≤ 5
x1 , x2 ≥ 0
1
Expert's answer
2020-04-30T20:22:38-0400

"x_1+x_2\\geq 6"

"3x_1+2x_2\\leq 30"

"2x_1+x_2\\leq 5"

"x_1, x_2\\geq 0"

Maximize "z=5x_1+8x_2"




Green region shows all solutions of "\\begin{cases}\nx_1+x_2\\geq 6\n\\\\3x_1+2x_2\\leq 30\n\\\\\n2x_1+x_2\\leq 5\n\\end{cases}"

And red region shows all solutions of "x_1,x_2\\geq 0"

We can see that there is no solution of the system "\\begin{cases}\nx_1+x_2\\geq 6\n\\\\3x_1+2x_2\\leq 30\n\\\\\n2x_1+x_2\\leq 5\n\\\\ x_1,x_2\\geq 0\n\\end{cases}" because intersection of these regions is empty.

Therefore, we can’t maximize "z=5x_1+8x_2" because there is no "(x_1,x_2)" , for which all inequalities are satisfied.


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