Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. LettingR = number of regular glovesCnumber of catcher's mitts-leads to the following formulation:Max 5R + 7℃s.t.3R + -C ≤ 1,0002-R + -C ≤ 3003-R + -C ≤ 1004R, C ≥ 0The computer solution is shown below.VariableRсOptimal Objective Value = 3550.00000Constraint123VariableRCCutting and sewingValue500.00000150.00000FinishingPackaging and shippingReduced Cost0.000000.00000Slack/Surplus275.000000.000000.000005.000007.00000Dual Value0.000004.5000022.00000Objective AllowableCoefficientIncrease5.500003.00000AllowableDecrease1.500003.66667 VariableRсConstraint123оооVariableRCConstraint123Value500.00000150.00000Slack/Surplus275.000000.000000.000005.000007.00000Reduced Cost0.000000.00000Objective AllowableCoefficientIncrease5.500003.00000RHSValue1000.00000300.00000100.00000Dual Value0.000004.5000022.00000AllowableIncreaseInfinite100.0000055.00000(b) Which constraints are binding? (Select all that apply.)cutting and sewingfinishingpackaging and shippingAllowableDecrease1.500003.66667(a) What is the optimal solution, and what is the value of the total profit contribution?regular glovecatcher's mittvalueAllowableDecrease275.00000166.6666725.00000

Answered: (a) What is the optimal solution, and…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Question

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 + 7℃
s.t.
3
R + -C ≤ 1,000
2
-R + -C ≤ 300
3
-R + -C ≤ 100
4
R, C ≥ 0
The computer solution is shown below.
Variable
R
с
Optimal Objective Value = 3550.00000
Constraint
1
2
3
Variable
R
C
Cutting and sewing
Value
500.00000
150.00000
Finishing
Packaging and shipping
Reduced Cost
0.00000
0.00000
Slack/Surplus
275.00000
0.00000
0.00000
5.00000
7.00000
Dual Value
0.00000
4.50000
22.00000
Objective Allowable
Coefficient
Increase
5.50000
3.00000
Allowable
Decrease
1.50000
3.66667

Variable
R
с
Constraint
1
2
3
ооо
Variable
R
C
Constraint
1
2
3
Value
500.00000
150.00000
Slack/Surplus
275.00000
0.00000
0.00000
5.00000
7.00000
Reduced Cost
0.00000
0.00000
Objective Allowable
Coefficient
Increase
5.50000
3.00000
RHS
Value
1000.00000
300.00000
100.00000
Dual Value
0.00000
4.50000
22.00000
Allowable
Increase
Infinite
100.00000
55.00000
(b) Which constraints are binding? (Select all that apply.)
cutting and sewing
finishing
packaging and shipping
Allowable
Decrease
1.50000
3.66667
(a) What is the optimal solution, and what is the value of the total profit contribution?
regular glove
catcher's mitt
value
Allowable
Decrease
275.00000
166.66667
25.00000

Expert Solution

Step 1 Introduction:-

Linear programming is a mathematical technique that is commonly used in the operations management departments of most companies. This technique is commonly used to find the best outcome with the maximum profit. Linear programming has various methods; each method is chosen by the companies as per their requirements or based on different factors.