a) Using the point drawing tool, plot all the corner points for the feasible area. The optimum solution is: X₁ = 20 (round your response to two decimal places). X₂= 20 (round your response to two decimal places). Optimal solution value Z = 40 (round your response to two decimal places). b) If a technical breakthrough occurred that raised the profit per unit of X₁ to $3, due to this change, the optimal solution changes As a result of the technical breakthrough, the optimum solution is: X₁ = 30 (round your response to two decimal places). X₂ = 0 (round your response to two decimal places). Optimal solution value Z= 90 (round your response to two decimal places). c) If the impact of technical breakthrough was incorrectly determined and instead of X, profit coefficient increasing to $3 it only increases to $1.25. As a result of this correction, the optimal solution found originally stays the same (...)

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Can you plot the points on the graph please.
Consider the following LP problem developed at Zafar Malik's Carbondale, Illinois, optical scanning firm:
Z=1X₁ + 1x₂
Maximize
Subject to:
2X₁ + 1x₂ ≤60
1X₁ + 2X₂ ≤60
X₁, X₂20
(C₁)
(C₂)
On the graph on right, constraints C, and C₂ have been plotted.
a) Using the point drawing tool, plot all the corner points for the feasible area.
The optimum solution is:
X₁ = 20 (round your response to two decimal places).
X1
X₂= 20 (round your response to two decimal places).
Optimal solution value Z = 40 (round your response to two decimal places).
b) If a technical breakthrough occurred that raised the profit per unit of X₁ to $3, due to this change, the optimal
solution changes
As a result of the technical breakthrough, the optimum solution is:
X₁ = 30 (round your response to two decimal places).
X₂ = 0 (round your response to two decimal places).
Optimal solution value Z= 90 (round your response to two decimal places).
c) If the impact of technical breakthrough was incorrectly determined and instead of X, profit coefficient
increasing to $3 it only increases to $1.25. As a result of this correction, the optimal solution found originally
stays the same
120-
110-
100-
90-
80-
70-
60-
50-
40-
30-
20-
104
04
0
AG1
Isoprofit Line!
3
10 20 30 40 50 60 70 80 90 100 110 120
X1
Q
ROO
Q
Transcribed Image Text:Consider the following LP problem developed at Zafar Malik's Carbondale, Illinois, optical scanning firm: Z=1X₁ + 1x₂ Maximize Subject to: 2X₁ + 1x₂ ≤60 1X₁ + 2X₂ ≤60 X₁, X₂20 (C₁) (C₂) On the graph on right, constraints C, and C₂ have been plotted. a) Using the point drawing tool, plot all the corner points for the feasible area. The optimum solution is: X₁ = 20 (round your response to two decimal places). X1 X₂= 20 (round your response to two decimal places). Optimal solution value Z = 40 (round your response to two decimal places). b) If a technical breakthrough occurred that raised the profit per unit of X₁ to $3, due to this change, the optimal solution changes As a result of the technical breakthrough, the optimum solution is: X₁ = 30 (round your response to two decimal places). X₂ = 0 (round your response to two decimal places). Optimal solution value Z= 90 (round your response to two decimal places). c) If the impact of technical breakthrough was incorrectly determined and instead of X, profit coefficient increasing to $3 it only increases to $1.25. As a result of this correction, the optimal solution found originally stays the same 120- 110- 100- 90- 80- 70- 60- 50- 40- 30- 20- 104 04 0 AG1 Isoprofit Line! 3 10 20 30 40 50 60 70 80 90 100 110 120 X1 Q ROO Q
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