# Linear programming problems:Graphical methods

In the following two problems: Provide the extreme points of the feasible region in the form of (x1 = , x2 = , Z = ) and identify which is the optimum solution. You need not list the origin as an extreme point, because it is a given. List the extreme points of the feasible region and indicate one of the following: (1) the optimal solutoin, (2) multiple optimal solutions, (3) unbounded problem, or (4) no feasible solution. If there is no feasible solution, then there would be no extreme points to show.

1) minimize Z = $3,000x1 + 1,000x2

subject to

60x1 + 20x2 > 1,200

10x1 + 10x2 > 400

40x1 + 160x2 > 2,400

x1, x2 > 0

2) minimize Z = 110x1 + 75x2

subject to

2x1 + x2 > 40

-6x1 + 8x2 > 120

70x1 + 105x1 > 2,100

x1, x2 > 0

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#### Solution Preview

In the following two problems: Provide the extreme points of the feasible region in the form of (x1 = , x2 = , Z = ) and identify which is the optimum solution. You need not list the origin as an extreme point, because it is a given. List the extreme points of the feasible region and indicate one of the following: (1) the optimal solutoin, (2) multiple optimal solutions, (3) unbounded ...

#### Solution Summary

This posting contains solution to following LPPs using graphical method.