Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The times (in minutes) required on each machine are as follows: Machine Component Shaper Grinder 1 7 5 2 5 5 3 5 2 The shaper is available for 125 hours, and the grinder is available for 95 hours. No more than 170 units of component 3 can be sold, but up to 1050 units of each of the other components can be sold. In fact, the company already has orders for 625 units of component 1 that must be satisfied. The profit contributions for components 1, 2, and 3 are $8, $6, and $9, respectively. If more time could be made available on the grinder, how much would it be worth? If required, round your answers to two decimal places.
Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The times (in minutes) required on each machine are as follows: Machine Component Shaper Grinder 1 7 5 2 5 5 3 5 2 The shaper is available for 125 hours, and the grinder is available for 95 hours. No more than 170 units of component 3 can be sold, but up to 1050 units of each of the other components can be sold. In fact, the company already has orders for 625 units of component 1 that must be satisfied. The profit contributions for components 1, 2, and 3 are $8, $6, and $9, respectively. If more time could be made available on the grinder, how much would it be worth? If required, round your answers to two decimal places.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The times (in minutes) required on each machine are as follows:
| Machine | ||
| Component | Shaper | Grinder |
| 1 | 7 | 5 |
| 2 | 5 | 5 |
| 3 | 5 | 2 |
The shaper is available for 125 hours, and the grinder is available for 95 hours. No more than 170 units of component 3 can be sold, but up to 1050 units of each of the other components can be sold. In fact, the company already has orders for 625 units of component 1 that must be satisfied. The profit contributions for components 1, 2, and 3 are $8, $6, and $9, respectively.
If more time could be made available on the grinder, how much would it be worth? If required, round your answers to two decimal places.
$ _____ per minute, since the dual value is _____ on the grinder at the optimal solution.
Transcribed Image Text:c. What are the right-hand-side ranges? If there is no lower or upper limit, then enter the text "NA" as your answer. If required, round your answers to the nearest whole number. If your answer is zero, enter "0".
$
Constraints lower limit
1
2
3
4
5
Right-Hand-Side-Range
6
7460 ✓
5090 ✔
0
✓
645 ✓
427
✓
ΝΑ ✓
upper limit
8310 ✔
5740
✓
183 ✓
ΝΑ ✓
NA ✔
645 ✔
Interpret the above ranges for company management.
The right-hand-side ranges are the ranges over which the dual values
✓ for the associated constraints are applicable.
d. If more time could be made available on the grinder, how much would it be worth? If required, round your answers to two decimal places.
3.60 X per minute, since the dual value is
3.60 X on the grinder at the optimal solution.
![Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The times (in minutes) required on each machine are as follows:
Component
1
2
3
Max
Shaper
7
5
s.t 7C1
5
The shaper is available for 125 hours, and the grinder is available for 95 hours. No more than 170 units of component 3 can be sold, but up to 1050 units of each of the other components can be sold. In fact, the company already has orders for
625 units of component 1 that must be satisfied. The profit contributions for components 1, 2, and 3 are $8, $6, and $9, respectively.
a. Formulate and solve for the recommended production quantities. If the constant is "1" it must be entered in the box.
8]v Ci]+
Let C₁ = units of component 1 manufactured
C₂ = units of component 2 manufactured
C3 units of component 3 manufactured
5 ✔ C₁+
1 ✓ C₁
1
Machine
✓ C1
Grinder
5
5
6
2
✓ C₂ +
5
✓ C₂+
5 C₂ + 2C3
1 ✓ C₂
C1,C2,C3 20
9 ✓ C3
5 ✓ C3 ≤
≤
1 ✔ C3 ≤
<
7,500 ✓ Constraint 1
5,700✔
170 ✓
Constraint 2
Constraint 3
1,050 ✓
Constraint 4
1,050 ✓
Constraint 5
625 ✔ Constraint 6](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2f2b6d9c-9995-46fc-b7bd-b3d175cbc6f7%2F4d239117-98de-407e-b600-297e8860061e%2Fuw62if9_processed.png&w=3840&q=75)
Transcribed Image Text:Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The times (in minutes) required on each machine are as follows:
Component
1
2
3
Max
Shaper
7
5
s.t 7C1
5
The shaper is available for 125 hours, and the grinder is available for 95 hours. No more than 170 units of component 3 can be sold, but up to 1050 units of each of the other components can be sold. In fact, the company already has orders for
625 units of component 1 that must be satisfied. The profit contributions for components 1, 2, and 3 are $8, $6, and $9, respectively.
a. Formulate and solve for the recommended production quantities. If the constant is "1" it must be entered in the box.
8]v Ci]+
Let C₁ = units of component 1 manufactured
C₂ = units of component 2 manufactured
C3 units of component 3 manufactured
5 ✔ C₁+
1 ✓ C₁
1
Machine
✓ C1
Grinder
5
5
6
2
✓ C₂ +
5
✓ C₂+
5 C₂ + 2C3
1 ✓ C₂
C1,C2,C3 20
9 ✓ C3
5 ✓ C3 ≤
≤
1 ✔ C3 ≤
<
7,500 ✓ Constraint 1
5,700✔
170 ✓
Constraint 2
Constraint 3
1,050 ✓
Constraint 4
1,050 ✓
Constraint 5
625 ✔ Constraint 6
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