# Linear Programming

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)

Answer: _____

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

Answer: _____

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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, ...

#### Solution Summary

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