MATH EXPERT ONLY.......

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P1

Sporting Goods
(a) Resource Requirements per Unit (b-1) Resource Requirements per Unit
Product Rubber (lb.) Leather (ft2) Product Rubber (lb.) Leather (ft2)
Basketball 3 4 Basketball 3 4
Football 2 5 Football 2 5
input Constraints
Total resources available 500 800 Total resources available 500 800
Basketball Football Basketball Football
Profits ($) 12 16 Profits ($) 13 16
Basketball Decision variables Basketball
Football Football
Maximized profits Objective function Maximized profits
(b-2) Resource Requirements per Unit (C-1) Resource Requirements per Unit
Product Rubber (lb.) Leather (ft2) Product Rubber (lb.) Leather (ft2)
Basketball 3 4 Basketball 3 4
Football 2 5 Football 2 5
input Constraints
Total resources available 500 800 Total resources available 1000 800
Basketball Football Basketball Football
Profits ($) 12 15 Profits ($) 12 16
Basketball Decision variables Basketball
Football Football
Maximized profits Objective function Maximized profits
Please use computer method to solve the problem (C-2) Resource Requirements per Unit
Please enter your solution in Yellow cells Product Rubber (lb.) Leather (ft2)
Basketball 3 4
Football 2 5
Total resources available 500 1300
Basketball Football
Profits ($) 12 16
Decision variables Basketball
Football
Objective function Maximized profits

P2

A & B products
Hours/ Unit
Product Line 1 Line2
A 12 4
B 4 8
Constraints Note: SUMPRODUCT(Col1, Col2) is a easier way to multiply
Total Hours 60 40 two rows or two columns
A B Standard Linear Programming: Maximixe 9 * A + 7 * B
Profits ($) 9 7 Subject to 12 * A + 4 * B <= 60
4 * A + 8 * B <= 40
Product A decision variables A >= 0
Product B B >= 0
Maximized profits Objective function

P3

A & B products
(a) Hours/ Unit (b) Hours/ Unit
Product Line 1 Line2 Product Line 1 Line2
A 12 4 A 12 4
B 4 8 B 4 8
Constraints
Total Hours 60 40 Total Hours 40 40
A B A B
Profits ($) 9 7 Profits ($) 9 7
Product A decision variables Product A
Product B Product B
Maximized profits Objective function Maximized profits
(c-1) Hours/ Unit
Product Line 1 Line2
A 12 4
B 4 8
Total Hours 60 40
A B
Profits ($) 9 15
Product A
Product B
Maximized profits
(c-2) Hours/ Unit
Product Line 1 Line2
A 12 4
B 4 8
Total Hours 60 40
A B
Profits ($) 9 20
Product A
Product B
Maximized profits

P4

Please run sensitivity analysis on P10 and enter the results (changes in coefficients of the objective function, and shadow prices) in YELLOW cells
Sensitivity analysis Min Max
Product A Coefficients in the objective function (profits for A and B)
Product B
Shadow price Additional Profits
Line 1
Line 2

P5

Irwin textile mills
(a) Corduroy denim
Profits for each product 3.1 2.25
Resources Available Resources Left over
Cotton 7.5 5 <= 6500
Labor 3.2 3 <= 3000
Demands
Corduroy <= 510 Demand met
denim <= 1000000 unlimited
Maximized profits
(b) Corduroy denim Corduroy denim
Profits for each product 3.1 3 Profits for each product 4 2.25
Resources Available Resources Resources Available Resources
Cotton 7.5 5 <= 6500 Cotton 7.5 5 <= 6500
Labor 3.2 3 <= 3000 Labor 3.2 3 <= 3000
Demands Demands
Corduroy <= 510 Corduroy <= 510
denim <= 1000000 denim <= 1000000
Maximized profits Maximized profits
C Corduroy denim
Profits for each product 3.1 2.25
Resources Available Resources
Cotton 7.5 5 <= 6000
Labor 3.2 3 <= 3000
Demands
Corduroy <= 510
denim <= 1000000
Maximized profits

P6

Please run sensitivity analysis on P5 and answer the following questions.
a.       If Irwin Mills can obtain additional cotton or processing time, but not both, which should it select? How much? Explain your answer.
Answer:
b.       Identify the sensitivity ranges for the objective function coefficients and for the constraint quantity values.
Then explain the sensitivity range for the demand for corduroy.
Min Max
Corduroy Demand ranges

P7 & P8

United Aluminum company
Aluminum Grade Mill
1 2 constraints
High 6 2 >= 12
Medium 2 2 >= 8 Please note, this constraint is missing in the problem
Low 4 10 >= 5
Aluminum Grade Mill
1 2
Cost ($) 6000 7000
Mill #1
Mill #2
Minimize Cost ($)
a.       Identify and explain the shadow prices for each of the aluminum grade contract requirements.
Shadow Price
High
Medium
Low
b.       Identify the sensitivity ranges for the objective function coefficients and the constraint quantity values.
Min Max
Mill #1
Mill #2
c. Aluminum Grade Mill
1 2 constraints
High 6 2 >= 20
Medium 2 2 >= 8
Low 4 10 >= 5
Aluminum Grade Mill
1 2
Cost ($) 6000 7000
Mill #1
Mill #2
Minimize Cost ($)

P9

Burger Doodle franchise
Biscuit Labor (hr.) Sausage (lb.) Ham (lb.) Flour (lb.)
Sausage 0.01 0.1 --- 0.04
Ham 0.024 --- 0.15 0.04
Constraints
6 30 30 16
Sausage Ham
Profits ($) 0.6 0.5
Sausage
Ham
Maximize Profits