HW4 Solution F11 (1) - Problem 6.2 a. A < B, A...

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Unformatted text preview: Problem 6.2 a. A < B, A < C or 2A < B + C b. 1 - A < B, 1 - A < C or 2(1 -A) < B + C c. 1 - A < 1 - B, 1 - A < 1 - C or 2(1 - A) < (1 - B) + (1 - C) d. IF A AND not B THEN Not C yields: A + (1 - B) - 1 < (1 - C) IF A AND not B THEN Not D yields: A + (1 - B) -1 < (1 - D) or 2(A + (1 - B)) -2 < (1 - C) + (1 - D) Problem 6.3 a. X1 + X2 < 50A + 100(1 - A) b. X1 + X2 > 50A + 10(1 - A) Problem 6.25 Hyvee Store Placement Minneapolis St Paul East West South North East West South North 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 3 Budget ($Millions) 2 2.5 3.2 4 3 3.8 4.5 2.8 12 Annual Profit ($1,000) 200 220 350 440 230 260 610 230 Build (1 = Yes, 0 = No) 1 1 1 Constraints LHS RHS 2 > 1 2 < 3 1 > 1 1 < 3 Budget ($Millions) 11.7 < 12 Annual Profit ($1,000) $1,400 > 1 Minneapolis < 3 Minneapolis > 1 St Paul < 3 St Paul > 1 Minneapolis < 3 Minneapolis > 1 St Paul < 3 St Paul Part a. Let Mi = 1 if a store is built in location i in Minnapolis and 0 otherwise. Let Si = 1 if a store is built in location i in St Paul and 0 otherwise. i = E, W, S, N Max: Annual Profit = 200ME + 220MW + 350MS + 440MN + 230SE + 260SW + 610SS + 230SN subject to: ME + MW + MS + MN > 1 Min Stores in Minneapolis ME + MW + MS + MN < 3 Max Stores in Minneapolis SE + SW + SS + SN > 1 Min Stores in St Paul SE + SW + SS + SN > 3 Max Stores in St Paul 2ME + 2.5MW + 3.2MS + 4MN + 3SE + 3.8SW + 4.5SS + 2.8SN < 12 Budget All variables are binary Part b. ME < MN or ME - MN < Part c. Let F = 1 if HyVee gets the financial support and 0 otherwise. New Budget Constraint: 2ME + 2.5MW + 3.2MS + 4MN + 3SE + 3.8SW + 4.5SS + 2.8SN - 2F < 12 New Constraint: 3F < SE + SW + SS + SN F is binary. P r o b le m 7 .1 0 O ld F a it h fu l G ro up 1 G ro up 2 O v e ra l (m inute s ) M e a n 5 4 8 0 M e a n 71.4 S td D e v 2.9 5 7.5 S td D e v 13.8 Ite ra tio n G ro up T im e 1 2 73.0 76 5 2 2 2 79 .8 216 3 3 1 5 8 .36 4 5 4 2 78 .730 4 5 1 5 4 .0 74 19 6 1 5 3.6 5 5 7 1 5 6 .6 5 8 6 5 8 2 6 8 .16 8 4 9 2 8 9 .5 9 79 10 1 5 6 .9 4 8 4 1 1 5 .30 9 8 3 12 2 8 0 .9 9 3 13 2 76 .5 8 75 14 2 74 .8 375 9 15 2 76 .5 70 9 6 16 2 8 0 .8 6 0 8 5 17 2 79 .4 9 4 8 5 18 1 5 4 .79 75 19 2 8 4 .19 39 20 1 5 3.4 28 0 8 21 1 5 2.4 25 0 8 2 2 7 .9 6 5 6 23 1 5 2.0 9 24 7 24 2 8 2.5 24 6 9 25 1 5 4 .28 2 2 26 2 75 .72738 27 1 5 2.8 0 4 28 2 8 5 .8 2 8 2 29 2 8 1.276 19 30 1 5 2.18 726 31 2 8 3.0 4 35 32 2 7 .9 6 4 6 7 3 1 5 7.0 74 8 34 2 8 0 .6 4 8 3 35 2 6 .8 26 79 36 2 8 5 .9 276 37 2 8 7.3235 38 1 5 3.6 23 9 39 1 5 4 .9 70 1 4 0 1 5 2.0 39 73 4 1 1 5 4 .4 0 6 9 4 2 2 7 .6 4 10 9 4 3 2 7 .6 1239 4 1 5 4 .6 178 1 4 5 2 73.26 9 4 6 2 8 7.275 3 4 7 2 8 3.24 8 18 4 8 1 5 9 .6 8 0 6 4 9 2 74 .38 25 8 5 0 2 6 9 .5 7121 5 1 1 5 3.74 0 4 7 5 2 2 8 1.9 5 18 3 5 3 2 6 7.35 9 74 5 4 1 5 3.214 8 2 5 2 71.6 5 326 5 6 2 8 7.5 14 5 7 2 73.30 10 1 5 8 1 5 4 .6 9 4 5 8 5 9 2 7 .6 3 0 8 6 0 1 5 4 .0 270 2 6 1 2 6 5 .7139 2 6 2 2 78 .15 8 7 6 3 2 8 1.2 13 6 4 2 74 .0 75 74 6 5 2 8 .9 38 4 6 6 1 4 9 .36 4 7 6 7 2 72.6 79 2 6 8 2 8 2.8 6 5 8 6 9 1 5 .6 5 4 7 70...
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This note was uploaded on 01/17/2012 for the course MGMT 306 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

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HW4 Solution F11 (1) - Problem 6.2 a. A < B, A...

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