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 6 4 2 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 800 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 unitscomponent 2 unitscomponent 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 blank to blank units component 2 blank to blank units component 3 blank to blank units Interpret these ranges for company management. Changes in the profit coefficients within these ranges will not cause a change in the optimal number of components to produce.Changes in the profit coefficients outside these ranges will not cause a change in the optimal number of components to produce. Changes in the profit coefficients within these ranges will cause changes in the optimal number of components to produce. (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 blank to blank grinder availability blank to blank max units of component 3 blank to blank max units of component 1 blank to blank max units of component 2 blank to blank existing orders for component 1 blank to blank 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 increases profits by $1.50.Nothing, since there are 300 minutes of slack time on the grinder at the optimal solution. Every additional minute on the grinder decreases profits by $1.Every additional minute on the grinder increases profits by $3. (e) If more units of component 3 can be sold by reducing the sales price by $4, should the company reduce the price? Yes. At that price, it would be profitable to produce 700 units of component 3.Yes. Every additional unit of component 3 increases profits by $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.

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 6 4 2 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 800 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 unitscomponent 2 unitscomponent 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 blank to blank units component 2 blank to blank units component 3 blank to blank units Interpret these ranges for company management. Changes in the profit coefficients within these ranges will not cause a change in the optimal number of components to produce.Changes in the profit coefficients outside these ranges will not cause a change in the optimal number of components to produce. Changes in the profit coefficients within these ranges will cause changes in the optimal number of components to produce. (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 blank to blank grinder availability blank to blank max units of component 3 blank to blank max units of component 1 blank to blank max units of component 2 blank to blank existing orders for component 1 blank to blank 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 increases profits by $1.50.Nothing, since there are 300 minutes of slack time on the grinder at the optimal solution. Every additional minute on the grinder decreases profits by $1.Every additional minute on the grinder increases profits by $3. (e) If more units of component 3 can be sold by reducing the sales price by $4, should the company reduce the price? Yes. At that price, it would be profitable to produce 700 units of component 3.Yes. Every additional unit of component 3 increases profits by $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.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter5: Network Models

Section: Chapter Questions

Problem 70P

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Related questions

Question

	Machine
Component	Shaper	Grinder
1	6	4
2	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 800 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 unitscomponent 2 unitscomponent 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 blank to blank units

component 2 blank to blank units

component 3 blank to blank units

Interpret these ranges for company management.

Changes in the profit coefficients within these ranges will not cause a change in the optimal number of components to produce.Changes in the profit coefficients outside these ranges will not cause a change in the optimal number of components to produce. Changes in the profit coefficients within these ranges will cause changes in the optimal number of components to produce.

(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 blank to blank

grinder availability blank to blank

max units of component 3 blank to blank

max units of component 1 blank to blank

max units of component 2 blank to blank

existing orders for component 1 blank to blank

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 increases profits by $1.50.Nothing, since there are 300 minutes of slack time on the grinder at the optimal solution. Every additional minute on the grinder decreases profits by $1.Every additional minute on the grinder increases profits by $3.

(e)

If more units of component 3 can be sold by reducing the sales price by $4, should the company reduce the price?

Yes. At that price, it would be profitable to produce 700 units of component 3.Yes. Every additional unit of component 3 increases profits by $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.

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