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 they plant change?
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