Consider the following LP problem developed at Zafar Malik’s Carbondale, Illinois, optical scanning firm:
Maximize profit: = $1x1 + $1x2
Subject to: $2x1 + $1x2 ≤ 100
$1x1 + $2x2 ≤ 100
a. What is the optimal solution to this problem?
b. If a technical breakthrough occurred that raised the profit per unit of X1 to $3, would this affect the optimal solution?
c. Instead of an increase in the profit coefficient X1 to $3, suppose that profit was overestimated and should only have been $1.25. Does this change the original optimal solution?
d. Based on your answer to c., are there any unused resources?
e. Based on your answer to c. (at $1.25 for variable x1), how much would profit increase in constraint # 2 if 75 was added to the RHS?
We solve the given problem in Excel using Excel Solver as shown below:
The above table in the form of formulas is shown below for better understanding and reference:
As seen from above, the optimal solution is x1 = 33.33 & x2 = 33.33
b. We will re-solve the problem with revised values as shown below:
Hence, the optimal solution will change as shown above, x1 = 50, x2 = 0, Total profit = $150
c. We will re-solve the problem with revised values as shown below:
Hence, the optimal solution will change as shown above, x1 = 33.33, x2 = 33.33 will remain same, Total profit = $75
d. Based on the above solution, there are no unused constraints as seen above since LHS = RHS from both constraints.
e. We will re-solve the problem with revised values as shown below:
Increase in profit between part c and part e = 93.75 - 75 = $18.75
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Consider the following LP problem developed at Zafar Malik’s Carbondale, Illinois, optical scanning firm: Maximize profit:...
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