The supervisor of a manufacturing plant is trying to determine how many of two parts, Part X and Part Y, are to be produced per day. Each part must be processed in three sections of the plant. The time required for the production along with the profit contribution for each part are given in the following table. Time Required (Minutes/Unit) Part X Part Y Available time (minutes) Section 1 Section 2 Section 3 50 18 30 0 80 3,600 45 2,500 22 1,200 Profit/Unit $2 $3 No more than 60 units of Part X and up to 70 units of Part Y can be produced daily. The company already has orders for 30 units of Part Y that must be satisfied. Develop an LP model and solve for the optimal production quantities. Obtain the sensitivity report to answer the following questions. a. What is the amount of change in the objective function value if we increase the production quantity of Part Y by 1 unit from the optimal solution? (provide your answer in numerical value only) b. If more time could be made available in Section 2, how much would the profit increase? (provide your answer in numerical value only) c. If we increase the available hours for Section 1 by 100 units, what would be the resulting change in profit? (provide your answer in numerical value only)
The supervisor of a manufacturing plant is trying to determine how many of two parts, Part X and Part Y, are to be produced per day. Each part must be processed in three sections of the plant. The time required for the production along with the profit contribution for each part are given in the following table. Time Required (Minutes/Unit) Part X Part Y Available time (minutes) Section 1 Section 2 Section 3 50 18 30 0 80 3,600 45 2,500 22 1,200 Profit/Unit $2 $3 No more than 60 units of Part X and up to 70 units of Part Y can be produced daily. The company already has orders for 30 units of Part Y that must be satisfied. Develop an LP model and solve for the optimal production quantities. Obtain the sensitivity report to answer the following questions. a. What is the amount of change in the objective function value if we increase the production quantity of Part Y by 1 unit from the optimal solution? (provide your answer in numerical value only) b. If more time could be made available in Section 2, how much would the profit increase? (provide your answer in numerical value only) c. If we increase the available hours for Section 1 by 100 units, what would be the resulting change in profit? (provide your answer in numerical value only)
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
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Transcribed Image Text:The supervisor of a manufacturing plant is trying to determine how many of two parts, Part X and Part Y, are to be produced per day. Each part must be processed in three sections of the plant. The time required for the production along
with the profit contribution for each part are given in the following table.
Time Required (Minutes/Unit)
Section 1 Section 2
50
30
Part X
Part Y
Available time (minutes)
80
0
3,600
45
2,500
Section 3
18
22
1,200
Profit/Unit
$2
$3
No more than 60 units of Part X and up to 70 units of Part Y can be produced daily. The company already has orders for 30 units of Part Y that must be satisfied. Develop an LP model and solve for the optimal production quantities.
Obtain the sensitivity report to answer the following questions.
a. What is the amount of change in the objective function value if we increase the production quantity of Part Y by 1 unit from the optimal solution? (provide your answer in numerical value only)
b. If more time could be made available in Section 2, how much would the profit increase? (provide your answer in numerical value only)
c. If we increase the available hours for Section 1 by 100 units, what would be the resulting change in profit? (provide your answer in numerical value only)
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