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# Linear Programming

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A. Minimization Graphical Solution
Solve the following linear programming model graphically and select the set of extreme points that make up the solution:
Minimize Z = 20X1 + 10X2
subject to:
X1 + X2 < 12
2X1 + 5X2 > 40
X2 < 13
Note: The triplets are in the form of (X1 = ,X2 = , Z = )

a) (0, 12, 120), (0, 8, 80), (20/3, 16/3, 560/3)

b) (0, 12, 240), (6, 5, 160), (20, 0, 200)

c) (12, 0, 120), (6, 5, 160), (0, 8, 160)

d) (12, 0, 120), (6, 5, 160), (20/3, 16/3, 560/3)

B. Minimization Graph Surplus Variables
Based on the optimal solution from the previous problem, which of the following statements is true if s1 represents the slack from the first constraint and s2 represents the slack from the second constraint?

a) Constraint 1 has no slack
Constraint 2 has no slack

b) Constraint 2 has no slack
Constraint 3 has no slack

c) Constraint 1 has no slack
Constraint 3 has no slack

https://brainmass.com/math/linear-programming/linear-programming-238138

#### Solution Preview

A. Minimization Graphical Solution
Solve the following linear programming model graphically and select the set of extreme points that make up the solution:
Minimize Z = 20X1 + 10X2
subject to:
X1 + X2 < 12
2X1 + 5X2 > 40
X2 < 13
Note: The triplets are in the form of (X1 = ,X2 = , Z = )

a) (0, 12, 120), (0, 8, 80), (20/3, 16/3, 560/3)

b) (0, 12, 240), (6, 5, 160), (20, 0, 200)

c) (12, 0, 120), (6, 5, 160), (0, 8, 160)

d) (12, 0, ...

#### Solution Summary

Solves Linear Programming problems using graphical solution and identifies slack from constraints.

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