Resource Requirements per Unit

P1

Sporting Goods
(a) Resource Requirements per Unit (c-1) Resource Requirements per Unit
Product Rubber (lb.) Leather (ft2) Product Rubber (lb.) Leather (ft2)
Basketball 2.8 3.7 Basketball 2.8 3.7
Football 1.5 5.2 Football 1.5 5.2
input Constraints
Total resources available 600 900 Total resources available 1000 900
Basketball Football Basketball Football
Profits ($) 11 15 Profits ($) 11 15
Basketball Decision variables Basketball
Football Football
Maximized profits Objective function Maximized profits
(b) Resource Requirements per Unit (C-2) Resource Requirements per Unit
Product Rubber (lb.) Leather (ft2) Product Rubber (lb.) Leather (ft2)
Basketball 2.8 3.7 Basketball 2.8 3.7
Football 1.5 5.2 Football 1.5 5.2
input Constraints
Total resources available 600 900 Total resources available 600 1500
Basketball Football Basketball Football
Profits ($) 12 15 Profits ($) 11 15
Basketball Decision variables Basketball
Football Football
Maximized profits Objective function Maximized profits
Please use computer method to solve the problem
Please enter your solution in Yellow cells

P2

A & B products
(a) Hours/ Unit
Product Line 1 Line2
A 11 5
B 6 9
Constraints
Total Hours 65 40
A B
Profits ($) 11 15
Product A decision variables
Product B
Maximized profits Objective function
(b) Sensitivity Range for the coefficient of # of units of product A in the objectivefunction
Sensitivity Range for the coefficient of # of units of product B in the objectivefunction
(c’) Shadow Price for additional hours of production time on Line 1
Shadow Price for additional hours of production time on Line 2
Which one of the two the company would prefer (Line 1 or Line 2?)

P3

Irwin textile mills
(a) Corduroy denim
Profits for each product 3.25 2.5
Resources Available Resources
Cotton 8 6 <= 6500
Labor 4 3 <= 3000
Demands
Corduroy <= 510
denim <= 1000000
Maximized profits
Write the standard form of the LP model in the space provided below
(b) How much extra cotton and processing time are left at the optimal solution?
Cotton
Processing Time
Is the demand for Corduroy met?
(‘c) If Irwin Mills can obtain additional cotton or processing time, but not both, which should it select? How much?
Processing Time or additional cottone?
How much?

P4

Bradley Family
(a) Let X1 = # of acres of corn and X2 = # of acres of tobacco
Corn Tobacco Resources Available
300 520
Land 1 1 <= 410
Budget 105 210 <= 52500
Govt. Restriction 0 1 <= 100 Government Restriction
X1 X2
Decision Variables
Objective function
(b) How many acres of farm land will not be cultivated at the optimal solution?
Do the Bradleys use the entire 100 acre tobacco allotment?
(‘c) Should the Bradleys’ lease extral land from their neighbor at $110 per acre?
What is the maximum price the Bradleys’ should pay their neighbor? And how much land shoud they lease?
maximum price
# of acres of land
(d) For each dollar they borrow , how much additional profit will they make?
If they borrowed a additional $1000, would the number of acres of corn and tobacco