lec7 - 15.053 Lecture 7 Sensitivity Analysis Created by...

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15.053 Lecture 7 Sensitivity Analysis Created by Mike Metzger *With help of Jim Orlin and Ollie the Owl **Guest Appearances by numerous celebrities 1
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What’s Going On? ± Where is Professor Orlin? ² Vegas? ² South Beach? ² Amsterdam? ² In the first row? ± Is he OK? ² He is feeling just fine! 2
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Inspirational Quote ± “On a more serious note, there's going to be a lot more information and updates on here in the coming weeks and I think this will provide you with the opportunity to get to know who I really am.” ² Kevin Federline ± Posted 6/8/05 ± Website not updated since 6/8/05 ± Too busy doing Simplex Method 3
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Quote of the Day ± "A computer only knows what it's been programmed to know. .., a mind can think up infinite possibilities." ² Carmen Sandiego 4
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Today’s Topic: Sensitivity Analysis ± Outline: ± Jessica is in trouble! ± Formulation ± Excel model ± Sensitivity Analysis ± Convexity ± Surprises- Guest Appearances! 5
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Our Problem ± A Recent Letter we received: Dear 15.053 Class, My name is Jessica Simpson. I have been going through some tough times recently and am having a real problem with one of my cosmetic lines. The info for the line is on the next page. Recently though costs are changing based on market demand in addition to highly fluctuating resource costs. My problem is this we currently have an LP that we solve to find the optimal amount to produce of each product. However, every time a parameter changes, I am always forced to resolve the LP and this takes too long. I was hoping you guys could find a better way. Lately I have just been out of it. For example, Nick and I decided to split our Hummer in half, and now I need to buy a new one. Oh yeah, about the LP it seems to have been misplaced when I was moving out of my Malibu house. Please Help! - Jessica 6
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Problem Data: See dessertbeauty.com ± Jessica sells four types of lip gloss. The resources needed to produce one unit of each are known. Creamy(1) Juicy (2) Dreamy (3) Sunny (4) Raw material 2 3 4 7 Hours of labor 3 4 5 6 Sale price $4 $6 $7 $8 ± Exactly 950 total units must be produced. ± Customers demand that at least 400 units of product 4 be produced. ± Formulate an LP to maximize profit. ± Raw Materials Available <=4600 ± Labor Available <=5000 7
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Task 1-Formulate the LP ± Remember the Three Parts! ² Decision variables ² Objective ² Constraints Don’t Forget Non Negativity. Isn't that my job, to remind them of things? 8
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Our LP ± Define: ² X 1 = Amount of Creamy Gloss produced ² X 2 = Amount of Juicy Gloss produced ² X 3 = Amount of Dreamy Gloss produced ² X 4 = Amount of Sunny Gloss produced Max : z = 4 x 1 + 6 x 2 + 7 x 3 + 8 x 4 subject to : x 1 + x 2 + x 3 + x 4 = 950 x 4 400 2 x 1 + 3 x 2 + 4 x 3 + 7 x 4 4600 3 x 1 + 4 x 2 + 5 x 3 + 6 x 4 5 0 0 0 ,,, 0 xxxx 1 2 3 4 9
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Solving The Initial LP ± Which Method?
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lec7 - 15.053 Lecture 7 Sensitivity Analysis Created by...

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