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A core Course on Modeling

A core Course on Modeling. Introduction to Modeling 0LAB0 0LBB0 0LCB0 0LDB0 c.w.a.m.v.overveld@tue.nl v.a.j.borghuis@tue.nl S.19. Example 3:. “ How can we get rich selling peanut butter ?”. http://commons.wikimedia.org/wiki/File:PeanutButter.jpg. relations. dimensions. todo.

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A core Course on Modeling

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  1. A core Course on Modeling Introductionto Modeling 0LAB0 0LBB0 0LCB0 0LDB0 c.w.a.m.v.overveld@tue.nl v.a.j.borghuis@tue.nl S.19

  2. Example 3: • “How can we get rich • sellingpeanutbutter?” http://commons.wikimedia.org/wiki/File:PeanutButter.jpg

  3. relations dimensions todo assumptions profit income expenses pricePerItem nrSoldItems nrSoldTotal marketShare profit = income - expenses [Euro / year] = [Euro/year] no taxes, no inflation no discount with larger quantities per purchase income = pricePerItem * nrSoldItems [Euro / year] = [Euro/myPB] * [myPB/year] my PB will not increase the total market nrSoldItems = nrSoldTotal * marketShare [myPB / year] = [allPB / year] * [myPB/allPB] http://www.watnouweg.nl/nieuws/nieuwsitem.php?id=348&back=1&page=29 nrSoldTotal = 2x107[allPB/year] pricePerItem = … marketShare = …

  4. Dependency: • how does marketShare • depend on pricePerItem? http://www.sxc.hu/browse.phtml?f=download&id=366244

  5. marketShare 1 0 • pricePerItem Approach 1: Glass Box ?

  6. QUIZ How does market share depend on price per item? How canthisrelationbeexpressed in a mathematicalformula?

  7. marketShare 1 0 • pricePerItem Approach 1: Glass Box ? • WhatmechanismdeterminesmarketShare(pricePerItem)? • monotonicallydecreasing • between 0 and 1 • asymptote: marketShare0 ifpricePerItem  • asymptote: marketShare1 ifpricePerItem -  • whatsort of mathematicaldependency ???

  8. 1st guess: straight lines • advantage: simple • disadvantage: not smooth • uncertainifthisfollowsthe actualbehavior • cheapest • competitor • most expensive • competitor • marketShare 1 0 • pricePerItem Approach 1: Glass Box • WhatmechanismdeterminesmarketShare(pricePerItem)? • monotonicallydecreasing • between 0 and 1 • asymptote: marketShare0 ifpricePerItem  • asymptote: marketShare1 ifpricePerItem -  • whatsort of mathematicaldependency ???

  9. 2nd, 3rd guess: arctan, logistic, …? • advantage: smooth • disadvantage: more parameters? • whatvaluesfor the parameters? • uncertainifthisfollows the actualbehaviour • cheapest • competitor • most expensive • competitor • marketShare 1 0 • pricePerItem Approach 1: Glass Box • WhatmechanismdeterminesmarketShare(pricePerItem)? • monotonicallydecreasing • between 0 and 1 • asymptote: marketShare0 ifpricePerItem  • asymptote: marketShare1 ifpricePerItem -  • whatsort of mathematicaldependency ???

  10. cheapest • competitor • most expensive • competitor • marketShare 1 0 • pricePerItem Approach 2: Black Box • WhatmechanismdeterminesmarketShare(pricePerItem)? • monotonicallydecreasing • between 0 and 1 • asymptote: marketShare0 ifpricePerItem  • asymptote: marketShare1 ifpricePerItem -  • whatsort of mathematicaldependency ???

  11. cheapest • competitor • most expensive • competitor • marketShare 1 0 • pricePerItem Approach 2: Black Box ask a panel iftheywouldpay € ... for your PB • WhatmechanismdeterminesmarketShare(pricePerItem)? • monotonicallydecreasing • between 0 and 1 • asymptote: marketShare0 ifpricePerItem  • asymptote: marketShare1 ifpricePerItem -  • whatsort of mathematicaldependency ???

  12. cheapest • competitor • most expensive • competitor • marketShare 1 0 • pricePerItem Approach 2: Black Box ask a panel iftheywouldpay € ... for your PB • WhatmechanismdeterminesmarketShare(pricePerItem)? • monotonicallydecreasing • between 0 and 1 • asymptote: marketShare0 ifpricePerItem  • asymptote: marketShare1 ifpricePerItem -  • whatsort of mathematicaldependency ???

  13. Summary: • while making a model: • encouter a new quantity • ask: what does itdepend on • ask: how does the dependency look like

  14. Summary: • while making a model: • encouter a new quantity • ask: what does itdepend on • ask: how does the dependency look like • known or assumedmechanism: glass box http://www.sxc.hu/browse.phtml?f=download&id=596438

  15. Summary: • while making a model: • encouter a new quantity • ask: what does itdepend on • ask: how does the dependency look like • known or assumedmechanism: glass box • measure or guessed data: black box • data mayneed a smooth interpolation http://www.sxc.hu/browse.phtml?f=download&id=36217

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