Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. Letting R = number of regular gloves C = number of catcher's mitts leads to the following formulation: Max 5R + 8C s.t. R + 3 2C ≤ 800 Cutting and sewing 1 2R + 1 3C ≤ 240 Finishing 1 8R + 1 4C ≤ 100 Packaging and shipping R, C ≥ 0 The computer solution is shown below. Optimal Objective Value = 3520.00000 Variable Value Reduced Cost R 320.00000 0.00000 C 240.00000 0.00000 Constraint Slack/Surplus Dual Value 1 120.00000 0.00000 2 0.00000 3.00000 3 0.00000 28.00000 Variable Objective Coefficient Allowable Increase Allowable Decrease R 5.00000 7.00000 1.00000 C 8.00000 2.00000 4.66667 Constraint RHS Value Allowable Increase Allowable Decrease 1 800.00000 Infinite 120.00000 2 240.00000 160.00000 106.66667 3 100.00000 24.00000 40.00000 (a) Determine the objective coefficient ranges. (Round your answers to two decimal places.) regular glove to catcher's mitt to (b) Interpret the ranges in part (a). (Round your answers to two decimal places.) As long as the profit contribution for the regular glove is between $ and $ , the current solution optimal. As long as the profit contribution for the catcher's mitt is between $ and $ , the current solution optimal. (c) Interpret the right-hand-side ranges. The dual values for the resources are applicable over the following ranges. (Round your answers to two decimal places. If there is no upper or lower limit, enter NO LIMIT.) cutting and sewing to finishing to packaging and shipping to (d) How much will the value of the optimal solution improve (in $) if 10 extra hours of packaging and shipping time are made available?
Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. Letting R = number of regular gloves C = number of catcher's mitts leads to the following formulation: Max 5R + 8C s.t. R + 3 2C ≤ 800 Cutting and sewing 1 2R + 1 3C ≤ 240 Finishing 1 8R + 1 4C ≤ 100 Packaging and shipping R, C ≥ 0 The computer solution is shown below. Optimal Objective Value = 3520.00000 Variable Value Reduced Cost R 320.00000 0.00000 C 240.00000 0.00000 Constraint Slack/Surplus Dual Value 1 120.00000 0.00000 2 0.00000 3.00000 3 0.00000 28.00000 Variable Objective Coefficient Allowable Increase Allowable Decrease R 5.00000 7.00000 1.00000 C 8.00000 2.00000 4.66667 Constraint RHS Value Allowable Increase Allowable Decrease 1 800.00000 Infinite 120.00000 2 240.00000 160.00000 106.66667 3 100.00000 24.00000 40.00000 (a) Determine the objective coefficient ranges. (Round your answers to two decimal places.) regular glove to catcher's mitt to (b) Interpret the ranges in part (a). (Round your answers to two decimal places.) As long as the profit contribution for the regular glove is between $ and $ , the current solution optimal. As long as the profit contribution for the catcher's mitt is between $ and $ , the current solution optimal. (c) Interpret the right-hand-side ranges. The dual values for the resources are applicable over the following ranges. (Round your answers to two decimal places. If there is no upper or lower limit, enter NO LIMIT.) cutting and sewing to finishing to packaging and shipping to (d) How much will the value of the optimal solution improve (in $) if 10 extra hours of packaging and shipping time are made available?
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter3: Introduction To Optimization Modeling
Section: Chapter Questions
Problem 1C
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Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. Letting
- R = number of regular gloves
- C = number of catcher's mitts
leads to the following formulation:
Max | 5R | + | 8C | |||||||
s.t. | ||||||||||
R | + |
|
≤ | 800 | Cutting and sewing | |||||
|
+ |
|
≤ | 240 | Finishing | |||||
|
+ |
|
≤ | 100 | Packaging and shipping | |||||
R, | C | ≥ 0 |
The computer solution is shown below.
Optimal Objective Value = 3520.00000
Variable | Value | Reduced Cost |
R | 320.00000 | 0.00000 |
C | 240.00000 | 0.00000 |
Constraint | Slack/Surplus | Dual Value |
1 | 120.00000 | 0.00000 |
2 | 0.00000 | 3.00000 |
3 | 0.00000 | 28.00000 |
Variable | Objective Coefficient |
Allowable Increase |
Allowable Decrease |
R | 5.00000 | 7.00000 | 1.00000 |
C | 8.00000 | 2.00000 | 4.66667 |
Constraint | RHS Value |
Allowable Increase |
Allowable Decrease |
1 | 800.00000 | Infinite | 120.00000 |
2 | 240.00000 | 160.00000 | 106.66667 |
3 | 100.00000 | 24.00000 | 40.00000 |
(a)
Determine the objective coefficient ranges. (Round your answers to two decimal places.)
regular glove to catcher's mitt to
(b)
Interpret the ranges in part (a). (Round your answers to two decimal places.)
As long as the profit contribution for the regular glove is between $ and $ , the current solution optimal. As long as the profit contribution for the catcher's mitt is between $ and $ , the current solution optimal.
(c)
Interpret the right-hand-side ranges.
The dual values for the resources are applicable over the following ranges. (Round your answers to two decimal places. If there is no upper or lower limit, enter NO LIMIT.)
cutting and sewing to finishing to packaging and shipping to
(d)
How much will the value of the optimal solution improve (in $) if 10 extra hours of packaging and shipping time are made available?
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