DMOR-04-03 -...

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UF-ESI-6314bf35e009fab178535aa325eafe98b713009edf31.xls Problem Statementpage 1 of 9 Luther Setzer 1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899 (321) 544-7435 Items Chips Ice Gatorade Beer Hot Dogs Bad-for-you 15 0 5 25 15 Preference 7 0 3 10 8 Questions 3 through 9 (5 points each). Now, the remaining questions are related to sensitivity analysis. Consider the following example. I am trying to figure out how to fill up my cooler for this weekend's tailgating party. I can fill it up with chips, ice, Gatorade, beer, and hot dogs. Let's measure the amount of each item that I put in the cooler by the % space of the cooler that it fills. I have to keep the Gatorade, beer, and hot dogs cold, so I need at least as much ice in the cooler as I have these three items. I'm going to get thirsty while I'm there, so I need to have at least 50% of the cooler filled with items that I can drink (ice counts as an item that I can drink, since it will melt). The "bad-for-you" value of each item, and my preference for each item, is given in the following table. I will put a hard constraint that I cannot have more than 10 total units of "bad-for-you" items in my cooler. Associate variables c , i , g , b , and h with these products (that's the percentage of space that each of these items takes up in my cooler). Hence, my optimization problem is formulated as follows. Maximize z = 7 c +0 i +3 g +10 b +8 h subject to 15 c +0 i +5 g +25 b +15 h ≤ 10 I will put a hard constraint that I cannot have more than 10 total units of "bad-for-you" items in my cooler. Add a slack variable s 1 . 1 c +1 i +1 g +1 b +1 h ≤ 1 I can fill it up with chips, ice, Gatorade, beer, and hot dogs. Let's measure the amount of each item that I put in the cooler by the % space of the cooler that it fills. Add a slack variable s 2 . 0 c +1 i -1 g -1 b -1 h ≥ 0 I have to keep the Gatorade, beer, and hot dogs cold, so I need at least as much ice in the cooler as I have these three items. Subtract a slack variable s 3 . 0 c +1 i +1 g +1 b +0 h ≥ 0.5 I'm going to get thirsty while I'm there, so I need to have at least 50% of the cooler filled with items that I can drink (ice counts as an item that I can drink, since it will melt). Subtract a slack variable s 4 . c , i , g , b , h ≥ 0
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UF-ESI-6314 bf35e009fab178535aa325eafe98b713009edf31.xls Standard Form page 2 of 9 Luther Setzer 1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899 (321) 544-7435 Begin by recasting these equations into standard form. maximize: subject to: Here's the optimal tableau. Basics z c i g b h RHS z 1.00 0.00 0.00 0.60 0.00 0.00 0.32 2.20 1.00 1.20 4.80 c 0.00 1.00 0.00 -1.60 0.00 0.00 0.08 -0.20 -1.00 0.80 0.20 i 0.00 0.00 1.00 0.80 0.00 0.00 -0.04 0.60 0.00 -0.40 0.40 b 0.00 0.00 0.00 0.20 1.00 0.00 0.04 -0.60 0.00 -0.60 0.10 h 0.00 0.00 0.00 1.60 0.00 1.00 -0.08 1.20 1.00 0.20 0.30 I presented this to my tailgating buddies, but they all had questions and complaints. Check the optimal tableau using standard simplex tool.
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DMOR-04-03 -...

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