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Homework_2_Solutions

# Homework_2_Solutions - k y ij = power sent from power plant...

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HOMEWORK 2 SOLUTIONS GRADERS: ANDREW LI (AAL2131, A-L) & LINWEI LI (LL2713, M-Z) 1. Problem 1 (a) Yes, (0 , 0) satisfies all constraints. 1 pts (b) Vertices: (0 , 0) , (1 , 0) , (0 , 1 5 ) 4 pts (c) x 1 = 1 , x 2 = 0. No better solution. 3 pts (d) No, an optimal solution may not lie in the interior of the feasible region. 2 pts 2. Problem 2 (a) x 1 = 8 , x 2 = 0 5 pts (b) 5 pts 1

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2 GRADERS: ANDREW LI (AAL2131, A-L) & LINWEI LI (LL2713, M-Z) max x 1 subject to: - x 1 + x 2 + s 1 = 2 x 1 + x 2 + s 2 = 8 - x 1 + x 2 + s 3 = 4 x 1 , x 2 , s 1 , s 2 , s 3 0 3. Problem 3 10 pts x ik = power generated by power plant P i at price level
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Unformatted text preview: k y ij = power sent from power plant P i to customer sector S j i = 1 , 2 , j = 1 , 2 , 3 , k = 1 , 2 , 3 min 10 x 11 + 20 x 12 + 25 x 13 + 8 x 21 + 10 x 22 + 28 x 23 subject to: y 11 + y 21 ≥ 4 y 12 + y 22 ≥ 7 y 13 + y 23 ≥ 6 x 11 + x 12 + x 13 = y 11 + y 12 + y 13 x 21 + x 22 + x 23 = y 21 + y 22 + y 23 x 11 ≤ 6 ,x 12 ≤ 2 ,x 13 ≤ 2 ,x 21 ≤ 3 ,x 22 ≤ 2 ,x 23 ≤ 6 x ik ≥ ,y ij ≥...
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