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 Machine Shaper 6 4 Grinder 4 5 3 4 2 The shaper is available for 120 hours, and the grinder is available for 110 hours. No more than 200 units of component 3 can be sold, but up to 1000 units of each of the other components can be sold. In fact, the company already has orders for 600 units of component 1 that must be satisfied. The profit contributions for components 1, 2, and 3 are $8, $6, and $9, respectively. a. write the LP model to maximize profit and solve it to find the optimal number of components and total profit. b. what are the objective function coefficient ranges for the three components? interpret these ranges for company management. c. what are the right hand side ranges for the shaper constraint? interpret the shadow price for this constraint and the right hand side for this constraint d. if more grinder time could be made available, how much would it be worth? e. if more units of component 3 can be produced, how much would an additional unit add to profit?
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 Machine Shaper 6 4 Grinder 4 5 3 4 2 The shaper is available for 120 hours, and the grinder is available for 110 hours. No more than 200 units of component 3 can be sold, but up to 1000 units of each of the other components can be sold. In fact, the company already has orders for 600 units of component 1 that must be satisfied. The profit contributions for components 1, 2, and 3 are $8, $6, and $9, respectively. a. write the LP model to maximize profit and solve it to find the optimal number of components and total profit. b. what are the objective function coefficient ranges for the three components? interpret these ranges for company management. c. what are the right hand side ranges for the shaper constraint? interpret the shadow price for this constraint and the right hand side for this constraint d. if more grinder time could be made available, how much would it be worth? e. if more units of component 3 can be produced, how much would an additional unit add to profit?
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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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
Machine
Shaper
6
4
Grinder
4
5
3
4
2
The shaper is available for 120 hours, and the grinder is available for 110 hours. No more than 200 units of
component 3 can be sold, but up to 1000 units of each of the other components can be sold. In fact, the
company already has orders for 600 units of component 1 that must be satisfied. The profit contributions for
components 1, 2, and 3 are $8, $6, and $9, respectively.
a. write the LP model to maximize profit and solve it to find the optimal number of components and total
profit.
b. what are the objective function coefficient ranges for the three components? interpret these ranges for
company management.
c. what are the right hand side ranges for the shaper constraint? interpret the shadow price for this
constraint and the right hand side for this constraint
d. if more grinder time could be made available, how much would it be worth?
e. if more units of component 3 can be produced, how much would an additional unit add to profit?
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