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# Linear programming

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For all linear programming problems, the implied non-negativity constraint is assumed. Don't forget to include this constraint if you are using Excel to solve any of these problems.

1. Linear Programming Properties
Which of the following statements is not true?

a) An infeasible solution violates all constraints.
b) A feasible solution point does not have to lie on the boundary of the feasible solution.
c) A feasible solution satisfies all constraints.
d) An optimal solution satisfies all constraints.

2. Minimization Graphical Solution
Solve the following linear model graphically and select the set of extreme points that make up the possible feasible solutions.

a) (x1=12, x2=0, z=120), (x1=6, x2=5, x3=160), (x1=0, x2=8, z=160)

b) (x1=0, x2=12, z=240), (x1=6, x2=5, x3=160), (x1=20, x2=0, z=200)

c) (x1=0, x2=12, z=240), (x1=20/3, x2=16/3, x3=520/3), (x1=20, x2=0, z=200)

d) (x1=12, x2=0, z=120), (x1=20/3, x2=16/3, x3=520/3), (x1=0, x2=8, z=160)

#### Solution Summary

This provides a variety of examples of working with solving linear programming problems.

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