# Consider the linear programming problem Maximize P = 2 x + 7 y Subject to 2 x + y ≥ 8 x + y ≥ 6 x ≥ 0 , y ≥ 0 a. Sketch the feasible set S . b. Find the corner points of S . c. Find the values of P at the corner points of S found in part (b). d. Show that the linear programming problem has no optimal solution. Does this contradict Theorem 2?

### Finite Mathematics for the Manager...

12th Edition
Soo T. Tan
Publisher: Cengage Learning
ISBN: 9781337405782

Chapter
Section

### Finite Mathematics for the Manager...

12th Edition
Soo T. Tan
Publisher: Cengage Learning
ISBN: 9781337405782
Chapter 3.3, Problem 62E
Textbook Problem
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## Consider the linear programming problemMaximize P = 2 x + 7 y Subject to 2 x + y ≥ 8 x + y ≥ 6 x ≥ 0 , y ≥ 0 a. Sketch the feasible set S .b. Find the corner points of S .c. Find the values of P at the corner points of S found in part (b).d. Show that the linear programming problem has no optimal solution. Does this contradict Theorem 2?

To determine

a)

To sketch:

The feasible set S.

### Explanation of Solution

Given:

The linear programming problem

Maximize P=2x+7y…… (1)

Subject to 2x+y8x+y6x0,y0

The planar region defined by the set of linear inequalities such that each point in this planar region is the feasible solution of the problem to be maximized or minimized is the feasible solution

To determine

(b)

To find:

The corner points of S.

To determine

(c)

To find:

The value of P at the corner points of S found in part (b).

To determine

(d)

To show:

The linear programming problem has no optimal solution.

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