Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a
ID: 409492 • Letter: K
Question
Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher"s model. The firm has 900 hours of production time available in its cutting and sewing department, 300 hours available in its finishing department, and 100 hours available in its packaging and shipping department. The production time requirements and the profit contribution per glove are given in the following table:
Production Time (hours)
Model
Cutting
and Sewing
Finishing
Packaging
and Shipping
Profit/Glove
Regular model
1
1/2
1/8
$5
Catcher`s model
3/2
1/3
1/4
$8
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 less than or equal to 900 cutting and sewing
1/2R+1/3C less than or equal to 300 finishing
1/8R+1/4C less than or equal to 100 packaging and shipping
The sensitivity report is shown in figure below.
FIGURE: THE SOLUTION FOR THE KELSON SPORTING EQUIPMENT PROBLEM
Optimal Objective Value = 3700.00000
Variable
Value
Reduced Cost
R
500.00000
0.00000
C
150.00000
0.00000
Constraint
Slack/Surplus
Dual Value
1
175.00000
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
900.00000
Infinite
175.00000
2
300.00000
100.00000
166.66667
3
100.00000
35.00000
25.00000
What is the optimal solution, and what is the value of the total profit contribution?
Optimal Solution
Regular Glove
Catcher's Mitt
Total Profit
$
Which constraints are binding?
Cutting and Sewing:
Finishing:
Packaging and shipping:
What are the shadow prices for the resources?
Cutting and Sewing:
Finishing:
Packaging and shipping:
Interpret each.
The shadow price is the value that............. the will change by if you increase the constraint by one unit. (choose the option for missing part )
1. objective function
2. variables, R and C,
3. slack or surplus
4. constraints 1, 2, and 3
Cutting and sewing has a shadow price of ..................... which means that if we add one hour to the cutting and sewing department the value of the objective function would ................. .( choose the options from listed below)
first missing part second missing part
a) 0 a) not change
b) 3 b) increase by $3
C) 28 c) increase by $28
d) 175 d) increase by $175
Finishing has a shadow price of........................... which means that if we add one hour to the finishing department the value of the objective function would ............................. .(Choose the options for missing parts of the sentence)
first missing part second missing part
a) 0 a) not change
b) 3 b) increase by $3
C) 28 c) increase by $28
d) 175 d) increase by $175
Packaging and shipping has a shadow price of ...............which means that if we add one hour to the packaging and shipping department the value of the objective function would................... . .(Choose the options for missing parts of the sentence)
first missing part second missing part
a) 0 a) not change
b) 3 b) increase by $3
C) 28 c) increase by $28
d) 175 d) increase by $175
Constraints with a shadow price of 0 means that..................... . .(Choose the options for missing parts of the sentence)
a) It is a binding constraint
b) It is a non-binding constraint
C) A mistake has been made
d) 0 hours of that constraint are used
d) If overtime can be scheduled in one of the departments, where would you recommend doing so? .(Choose the options for missing parts of the sentence)
a) Cutting and sewing
b) Cutting and sewing
C) Packaging and shipping
Production Time (hours)
Model
Cutting
and Sewing
Finishing
Packaging
and Shipping
Profit/Glove
Regular model
1
1/2
1/8
$5
Catcher`s model
3/2
1/3
1/4
$8
Explanation / Answer
Constraints with a shadow price of 0 means that..:
Answer: b) It is a non-binding constraint
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