IELM_assignment_3_solution

IELM_assignment_3_solution - IELM 202, Assignment #3...

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IELM 202, Assignment #3 Solution Due date: 26 October 2005, Wednesday, 12:00 noon Question 1 (20 marks): Consider the primal problem as below: Maximize Z = 2x 1 + x 2 Subject to: x 2 10 2x 1 + 5x 2 60 x 1 + x 2 18 3x 1 + x 2 44 and x 1 0, x 2 0 a). Construct the dual problem. Minimize V = 10y 1 + 60y 2 + 18y 3 + 44y 4 Subject to: 2y 2 + y 3 + 3y 4 2 y 1 + 5y 2 + y 3 + y 4 1 y i 0 for i = 1, 2, 3, 4 b). Use the fact that (x 1 , x 2 ) = (13, 5) is optimal for the primal problem to identify the nonbasic variables and basic variables for the optimal basis solution for the dual problem. When (x 1 , x 2 ) = (13, 5) is substituted into the primal constraints, 5 10 2(13) + 5(5) = 51 60 13 + 5 = 18 3(13) + 5 = 44 Therefore, the following constraints are bounded: x 1 + x 2 18 3x 1 + x 2 44 We concluded that y 3 , y 4 are basic variable and y 1 , y 2 , y 5 , y 6 are nonbasic variable for the dual problem.
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Question 2 (30 marks) : Consider the primal problem as below: Maximize Z = 3x 1 + 7x 2 + 2x 3 Subject to: -2x 1 + 2x 2 + x 3 10 3x 1 + x 2 - x 3 20 and x 1 0, x
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This note was uploaded on 01/05/2011 for the course IELM IELM202 taught by Professor D during the Fall '10 term at HKUST.

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IELM_assignment_3_solution - IELM 202, Assignment #3...

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