3_Tutorial_Exercises_Solution

3_Tutorial_Exercises_Solution - Integer Programming Chapter...

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Unformatted text preview: Integer Programming Chapter 5 Q13. Solution Let X1, X2 = numbers of salespeople assign region 1 and region 2 respectively Y1 = 0 if no sales office in region 1, and 1 if sales office opened in region 1 Max z = 85000X1 + 60000X2 - 18000 Y1 s.t. : X1 + X2 10 10000X1 + 7000X2 72000 X1 - 10 Y1 0 Xi 0 Xi = integer Y1 = 0 or 1 Q19. Solution Let X1, X2, X3 = number of salespeople allocate to Alsace, Bourgogne, and le-de-France respectively Max z = 25000X1 + 18000X2 + 31000X3 s.t. : 5000X1 + 11000X2 + 7000X3 700000 X1 + X2 + X3 = 100 Xi 10 Xi 0 Xi = integer Q15 Solution Let F1, F2, F3, F4, F5, F6 = number of employees working at Midnight, 4:00am, 8:00am, Noon, 4:00pm and 8:00pm respectively Min z = F1 + F2+ F3+ F4+ F5+ F6 s.t. : F1 + F6 90 F1 + F2 215 F2 + F3 250 F3 + F4 65 F4 + F5 300 F5 + F6 125 Fi 0 Fi = integer Q22. Solution Let X i be the selection decision for each course. i = 1-7 X i = 1 if course i is selected; X i = 0 if course i is not selected Minimize no. of hours, Z = 5 X 1 + 10 X 2 + 8 X 3 + 12 X 4 + 7 X 5 + 10 X 6 + 8 X 7 subject to: X1 - X 4 - X 6 + X 7 0 (minimum GPA requirement) From [ (9 X 1 + 6 X 2 + 6 X 3 + 3 X 4 + 6 X 5 + 3 X 6 + 9 X 7 ) /[3 * ( X 1 + X 2 + X 3 + X 4 + X 5 + X 6 + X 7 )] 2 3( X 1 + X 2 + X 3 + X 4 + X 5 + X 6 + X 7 ) 12 X2 + X3 + X4 + X6 2 X1 + X 2 + X 6 + X 7 3 X i = 0 or 1 (credit requirement) (course requirement) (course requirement) Q18. Solution Let X1, X2, X3 = number of denim jeans, CD players and Compact discs respectively Max z = 90X1 + 150X2 + 30X3 s.t. : 2X1 + 3X2 + X3 5 Xi 0 Xi = integer ...
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