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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: Component 1 2 3 Shaper 6 4 Machine 4 Grinder 4 5 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 900 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. to to to (a) Formulate and solve for the recommended production quantities. component 1 units component 2 units component 3 units (b) What are the objective coefficient ranges for the three components? (If there is no upper or lower limit, enter NO LIMIT. Round your answers to the nearest integer.) component 1 component 2 component 3 units units units

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 Shaper 6 4 Machine 4 Grinder 4 5 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 900 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. to to to (a) Formulate and solve for the recommended production quantities. component 1 units component 2 units component 3 units (b) What are the objective coefficient ranges for the three components? (If there is no upper or lower limit, enter NO LIMIT. Round your answers to the nearest integer.) component 1 component 2 component 3 units units units

Practical Management Science
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: Component Shaper 1 2 3 6 4 Machine 4 Grinder 4 LO 5 to to to 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 900 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) Formulate and solve for the recommended production quantities. component 1 units component 2 units component 3 units (b) What are the objective coefficient ranges for the three components? (If there is no upper or lower limit, enter NO LIMIT. Round your answers to the nearest integer.) component 1 component 2 component 3 units units units
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 Shaper 1 2 3 6 4 Machine 4 Grinder 4 LO 5 to to to 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 900 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) Formulate and solve for the recommended production quantities. component 1 units component 2 units component 3 units (b) What are the objective coefficient ranges for the three components? (If there is no upper or lower limit, enter NO LIMIT. Round your answers to the nearest integer.) component 1 component 2 component 3 units units units
(c) What are the right-hand-side ranges? (Use minutes for time. If there is no upper or lower limit, enter NO LIMIT. Round your answers to the nearest integer.) shaper availability grinder availability max units of component 3 max units of component 1 max units of component 2 existing orders for component 1 2 99 299 oooo to to to to to to Interpret these ranges for company management. These are the ranges over which the dual values for the associated constraints are not applicable. These are the ranges over which the reduced costs for the associated constraints are not applicable. These are the ranges over which the dual values for the associated constraints are applicable. These are the ranges over which the reduced costs for the associated constraints are applicable. (d) If more time could be made available on the grinder, how much would it be worth? Every additional minute on the grinder decreases profits by $1. Every additional minute on the grinder increases profits by $3. Every additional minute on the grinder increases profits by $1.50. Nothing, since there are 300 minutes of slack time on the grinder at the optimal solution. (e) If more units of component 3 can be sold by reducing the sales price by $4, should the company reduce the price? Yes. Every additional unit of component 3 increases profits by $3. Yes. At that price, it would be profitable to produce 700 units of component 3. No. There is a slack of 300 units so selling more would not improve profits. No. At that price, it would not be profitable to produce any of component 3.
Transcribed Image Text:(c) What are the right-hand-side ranges? (Use minutes for time. If there is no upper or lower limit, enter NO LIMIT. Round your answers to the nearest integer.) shaper availability grinder availability max units of component 3 max units of component 1 max units of component 2 existing orders for component 1 2 99 299 oooo to to to to to to Interpret these ranges for company management. These are the ranges over which the dual values for the associated constraints are not applicable. These are the ranges over which the reduced costs for the associated constraints are not applicable. These are the ranges over which the dual values for the associated constraints are applicable. These are the ranges over which the reduced costs for the associated constraints are applicable. (d) If more time could be made available on the grinder, how much would it be worth? Every additional minute on the grinder decreases profits by $1. Every additional minute on the grinder increases profits by $3. Every additional minute on the grinder increases profits by $1.50. Nothing, since there are 300 minutes of slack time on the grinder at the optimal solution. (e) If more units of component 3 can be sold by reducing the sales price by $4, should the company reduce the price? Yes. Every additional unit of component 3 increases profits by $3. Yes. At that price, it would be profitable to produce 700 units of component 3. No. There is a slack of 300 units so selling more would not improve profits. No. At that price, it would not be profitable to produce any of component 3.
Expert Solution
Step 1

Decision Variables:

Suppose-C1 be the unit of component 1 manufacturedC2 be the unit of component 2 manufacturedC3 be the unit of component 3 manufactured

 

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