you are given the following data for a linear programming problem where theobjective is to minimize the cost of conducting two nonnegative activities so as to achievethree benefits that do not fall below their minimum levels. Benefit Contribution per Unit of Each Activity Minimum Acceptable Level Benefit Activity 1 Activity 2 1 5 3 60 2 2 30 7 126 Unit cost $60 $50 (a) Formulate a linear programming model for this problem. (b) Use the graphical method to solve this model. I am confused with the sensitivity analysis part: (c) What is the sensitivity range of the unit cost of activity 1? Please calculate the optimalobjective value if we change the unit cost of activity 1 to 80. What if we change the unitcost of activity 1 to 90? (Hint: You can use excel or python to solve the problem.)
you are given the following data for a linear programming problem where theobjective is to minimize the cost of conducting two nonnegative activities so as to achievethree benefits that do not fall below their minimum levels. Benefit Contribution per Unit of Each Activity Minimum Acceptable Level Benefit Activity 1 Activity 2 1 5 3 60 2 2 30 7 126 Unit cost $60 $50 (a) Formulate a linear programming model for this problem. (b) Use the graphical method to solve this model. I am confused with the sensitivity analysis part: (c) What is the sensitivity range of the unit cost of activity 1? Please calculate the optimalobjective value if we change the unit cost of activity 1 to 80. What if we change the unitcost of activity 1 to 90? (Hint: You can use excel or python to solve the problem.)
Practical Management Science
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![you are given the following data for a linear programming problem where theobjective is to minimize the cost of conducting two nonnegative
activities so as to achievethree benefits that do not fall below their minimum levels.
Benefit Contribution per
Unit of Each Activity
Minimum
Acceptable
Level
Benefit
Activity 1
Activity 2
1
5
60
2
2
30
3
126
Unit cost
$60
$50
(a) Formulate a linear programming model for this problem.
(b) Use the graphical method to solve this model.
I am confused with the sensitivity analysis part:
(c) What is the sensitivity range of the unit cost of activity 1? Please calculate the optimalobjective value if we change the unit cost of activity 1
to 80. What if we change the unitcost of activity 1 to 90? (Hint: You can use excel or python to solve the problem.)
(d) What is the sensitivity range of the minimum acceptable level of benefit 3? Pleasecalculate the optimal objective value if change the
minimum acceptable level of benefit 3 to 130. What if we change the minimum acceptable level of benefit 3 to 110?
(e) What is the sensitivity range of the unit cost of activity 2?
Suppose we change the unitcost of the two activities to 90for activity 1 and 80for activity 2. Are the new unit costs in the sensitivity range?
Does the optimal solution change? Is the sensitivity rangeapplicable when multiple parameters change?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5a9048fd-ee0c-41a5-9548-ebc6fbb7c6ee%2F16ff5189-2983-4532-a5fe-0303d3e48d31%2F9igw2ms_processed.png&w=3840&q=75)
Transcribed Image Text:you are given the following data for a linear programming problem where theobjective is to minimize the cost of conducting two nonnegative
activities so as to achievethree benefits that do not fall below their minimum levels.
Benefit Contribution per
Unit of Each Activity
Minimum
Acceptable
Level
Benefit
Activity 1
Activity 2
1
5
60
2
2
30
3
126
Unit cost
$60
$50
(a) Formulate a linear programming model for this problem.
(b) Use the graphical method to solve this model.
I am confused with the sensitivity analysis part:
(c) What is the sensitivity range of the unit cost of activity 1? Please calculate the optimalobjective value if we change the unit cost of activity 1
to 80. What if we change the unitcost of activity 1 to 90? (Hint: You can use excel or python to solve the problem.)
(d) What is the sensitivity range of the minimum acceptable level of benefit 3? Pleasecalculate the optimal objective value if change the
minimum acceptable level of benefit 3 to 130. What if we change the minimum acceptable level of benefit 3 to 110?
(e) What is the sensitivity range of the unit cost of activity 2?
Suppose we change the unitcost of the two activities to 90for activity 1 and 80for activity 2. Are the new unit costs in the sensitivity range?
Does the optimal solution change? Is the sensitivity rangeapplicable when multiple parameters change?
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