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Operations Management
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 6R  +  9C     s.t.             R  +  3 2C  ≤  1,000     Cutting and sewing   1 2R  +  1 3C  ≤  300      Finishing   1 8R  +  1 4C  ≤  100      Packaging and shipping   R, C ≥ 0     The computer solution is shown below. Optimal Objective Value = 4350.00000 Variable Value Reduced Cost R 500.00000 0.00000 C 150.00000 0.00000 Constraint Slack/Surplus Dual Value 1 275.00000 0.00000 2 0.00000 4.50000 3 0.00000 30.00000 Variable Objective Coefficient Allowable Increase Allowable Decrease R 6.00000 7.50000 1.50000 C 9.00000 3.00000 5.00000 Constraint RHS Value Allowable Increase Allowable Decrease 1 1000.00000 Infinite 275.00000 2 300.00000 100.00000 166.66667 3 100.00000 55.00000 25.00000 (a) What is the optimal solution, and what is the value of the total profit contribution? regular glove --  catcher's mitt -- value -- (b) Which constraints are binding? (Select all that apply.) cutting and sewing finishing packaging and shipping (c) What are the dual values for the resources? Interpret each.   constraint 1 Each additional hour of cutting and sewing will improve profits by $4.50 or Each additional hour of cutting and sewing will improve profits by $275.00 or Each additional hour of cutting and sewing will improve profits by $30.00 or Additional hours of cutting and sewing will not improve profits.   constraint 2 Each additional hour of finishing will improve profits by $4.50 or Each additional hour of finishing will improve profits by $275.00 or Each additional hour of finishing will improve profits by $30.00 or Additional hours of finishing will not improve profits.   constraint 3 Each additional hour of packing and shipping will improve profits by $4.50 or Each additional hour of packing and shipping will improve profits by $275.00 or Each additional hour of packing and shipping will improve profits by $30.00 or Additional hours of packing and shipping will not improve profits. (d) If overtime can be scheduled in one of the departments, where would you recommend doing so? cutting and sewing or finishing    or packaging and shipping

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 6R  +  9C     s.t.             R  +  3 2C  ≤  1,000     Cutting and sewing   1 2R  +  1 3C  ≤  300      Finishing   1 8R  +  1 4C  ≤  100      Packaging and shipping   R, C ≥ 0     The computer solution is shown below. Optimal Objective Value = 4350.00000 Variable Value Reduced Cost R 500.00000 0.00000 C 150.00000 0.00000 Constraint Slack/Surplus Dual Value 1 275.00000 0.00000 2 0.00000 4.50000 3 0.00000 30.00000 Variable Objective Coefficient Allowable Increase Allowable Decrease R 6.00000 7.50000 1.50000 C 9.00000 3.00000 5.00000 Constraint RHS Value Allowable Increase Allowable Decrease 1 1000.00000 Infinite 275.00000 2 300.00000 100.00000 166.66667 3 100.00000 55.00000 25.00000 (a) What is the optimal solution, and what is the value of the total profit contribution? regular glove --  catcher's mitt -- value -- (b) Which constraints are binding? (Select all that apply.) cutting and sewing finishing packaging and shipping (c) What are the dual values for the resources? Interpret each.   constraint 1 Each additional hour of cutting and sewing will improve profits by $4.50 or Each additional hour of cutting and sewing will improve profits by $275.00 or Each additional hour of cutting and sewing will improve profits by $30.00 or Additional hours of cutting and sewing will not improve profits.   constraint 2 Each additional hour of finishing will improve profits by $4.50 or Each additional hour of finishing will improve profits by $275.00 or Each additional hour of finishing will improve profits by $30.00 or Additional hours of finishing will not improve profits.   constraint 3 Each additional hour of packing and shipping will improve profits by $4.50 or Each additional hour of packing and shipping will improve profits by $275.00 or Each additional hour of packing and shipping will improve profits by $30.00 or Additional hours of packing and shipping will not improve profits. (d) If overtime can be scheduled in one of the departments, where would you recommend doing so? cutting and sewing or finishing    or packaging and shipping

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter6: Optimization Models With Integer Variables
Section: Chapter Questions
Problem 51P
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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 6R  +  9C    
s.t.          
  R  + 
3
2
C		  ≤  1,000     Cutting and sewing
 
1
2
R		  + 
1
3
C		  ≤  300      Finishing
 
1
8
R		  + 
1
4
C		  ≤  100      Packaging and shipping
  R, C ≥ 0    
The computer solution is shown below.
Optimal Objective Value = 4350.00000
Variable Value Reduced Cost
R 500.00000 0.00000
C 150.00000 0.00000
Constraint Slack/Surplus Dual Value
1 275.00000 0.00000
2 0.00000 4.50000
3 0.00000 30.00000
Variable Objective
Coefficient		 Allowable
Increase		 Allowable
Decrease
R 6.00000 7.50000 1.50000
C 9.00000 3.00000 5.00000
Constraint RHS
Value		 Allowable
Increase		 Allowable
Decrease
1 1000.00000 Infinite 275.00000
2 300.00000 100.00000 166.66667
3 100.00000 55.00000 25.00000
(a)
What is the optimal solution, and what is the value of the total profit contribution?
regular glove -- 
catcher's mitt --
value --
(b)
Which constraints are binding? (Select all that apply.)
cutting and sewing
finishing
packaging and shipping
(c)
What are the dual values for the resources? Interpret each.
 
constraint 1
Each additional hour of cutting and sewing will improve profits by $4.50
or
Each additional hour of cutting and sewing will improve profits by $275.00
or
Each additional hour of cutting and sewing will improve profits by $30.00
or
Additional hours of cutting and sewing will not improve profits.
 
constraint 2
Each additional hour of finishing will improve profits by $4.50
or
Each additional hour of finishing will improve profits by $275.00
or
Each additional hour of finishing will improve profits by $30.00
or
Additional hours of finishing will not improve profits.
 
constraint 3
Each additional hour of packing and shipping will improve profits by $4.50
or
Each additional hour of packing and shipping will improve profits by $275.00
or
Each additional hour of packing and shipping will improve profits by $30.00
or
Additional hours of packing and shipping will not improve profits.
(d)
If overtime can be scheduled in one of the departments, where would you recommend doing so?
cutting and sewing or
finishing    or
packaging and shipping
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