Individual Problem 6.docx - 1 Business Decision Analysis Name Atul Joshi SI 2018070974 Put Unit 7 BUSI 2013 Business Decision Analysis Yorkville

Individual Problem 6.docx - 1 Business Decision Analysis...

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1 Business Decision Analysis Name - Atul Joshi SI- 2018070974 Put Unit # 7 BUSI 2013 Business Decision Analysis Yorkville University – Vancouver Campus Instructor: Dr. Christian Tabi Amponsah Submission Date : 5/5 2019 Table of Contents
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1 Abstract
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2 Introduction Starts here but don’t write the word introduction. Type equation here.
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3 Problem 1 Answer 1 A) Max 30 x 1 + 25 x 2 s.t. 3 x 1 + 1.5 x 2 400 1.5 x 1 + 2 x 2 250 1 x 1 + 1 x 2 150 x 1 , x 2 0 and x 2 integer This Linear program is a mixed integer linear program because mixed integer linear program is a linear program in which some but not necessarily all, variable are required to be an integer. This linear program requires x 2 to be an integer but x 1 can assume any positive value. LP relaxation is the linear program that result from dropping the integer requirements for the variables in an integer lines Max 30 x 1 + 25 x 2 s.t. 3 x 1 + 1.5 x 2 400 1.5 x 1 + 2 x 2 250 1 x 1 + 1 x 2 150 x 1 , x 2 0
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4 B) Min 3 x 1 + 4 x 2 s.t 2 x 1 + 4 8 2 x 1 + 6 12 x 1 , x 2 0 and integer This linear program is a all integer liner program because an all integer linear program is a linear program with the additional requirement that all variable must be integer. This linear program requires x 1 and x 2 to be an integers. LP relaxation is the linear program that results from dropping the integer requirements for the variables in an integer linear program. Min 3 x 1 + 4 x 2 s.t 2 x 1 + 4 x 2 8 2 x 1 + 6 x 2 12 x 1 , x 2 0 Problem 3 Answer 3 Max 1 x 1 + 1 x 2 s.t 4 x 1 + 6 x 2 22 1 x 1 + 5 x 2 15 2 x 1 + 1 x 2 9
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5 x 1 , x 2 0 and integer Graphical representation of the constraint 16 14 12 10 (0,9) 8 2 x 1 + 1 x 2 9 Feasible region 6 (0,5) 4 x 1 + 6 x 2 22 4 (0,3.67) 1 x 1 + 5 x 2 15 2 (4.5,0) (5.5,0) (15,0) 0 2 4 6 8 10 12 14 16 B) Solving the LP relaxation
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6 Problem 3 X1 X2 Constrai n 4 6 22 1 5 15 2 1 9 Model Max 5 X1 X2 Optimal Solution 4 1 Constraint LHS RHS 1 22 <= 22 2 9 <= 15 3 9 <= 9 10 (0,9) 8 2 x 1 + 1 x 2 9 Feasible region 6 (0,5) 4 x 1 + 6 x 2 22 (4,1) (optimal point) 4 (0,3.67) 1 x 1 + 5 x 2 15 2 (4.5,0) (5.5,0) (15,0) 0 2 4 6 8 10 12
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