Chapter 3
Linear programming and sensitivity
analysis
Example /1
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Min Z= 6X1+3X2
S.t
2X1+4X2>=16
4X1+3X2>=24
• Solve the linear programming model using the
Graphical method to found the value of X1,X2,
and Z.
Answer of Example /1
Example /2
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Consider the following linear program:
MAX
Z = 60A + 50B
s.t. 10A + 20B ≤ 200
8A + 5B ≤ 80
A≥2
B≥5
Solve this linear program graphically and determine the
optimal quantities of A, B, and the value of Z.
Answer of Example /2
Example /3
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Consider the following minimization problem:
Min z = x1 + 2x2
s.t. x1 + x2 ≥ 300
2x1 + x2 ≥ 400
2x1 + 5x2 ≤ 750
x1, x2 ≥ 0
Which constraints are binding at the optimal
solution
Answer of Example 3
Assignment of chapter 3
Maximize Z= x1 + x2
subject to
x1 <=7
X1+ 5x2 <=5
X1,X2>=0
What is the value of Z
1. If Coefficient (OFC)of X1 change from 1 to 3?
2. If the parameter of X2 in constraint 1 change to 3?
3. If the parameter of X1 in constraint 2 change to 2?