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# lecture11-handout - ISyE 323 Lecture#11 Prof Je Linderoth...

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ISyE 323 Lecture #11 Prof. Jeﬀ Linderoth October 20, 2009

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ISyE Lecture #11 Outline Outline Economic Interpretation of Duality (Section 6.2) Primal–Dual Relationships (Section 6.3) Adapting to Other Primal Forms (Section 6.4) Sensitivity Analysis (Sections 6.5–6.8) ISyE Lecture #11 2
ISyE Lecture #11 Economic Interpretation of Duality (Section 6.2) Outline Economic Interpretation of Duality (Section 6.2) Get Me Some Bling Go To Excel Shadow Prices Primal–Dual Relationships (Section 6.3) Adapting to Other Primal Forms (Section 6.4) Sensitivity Analysis (Sections 6.5–6.8) ISyE Lecture #11 3

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ISyE Lecture #11 Economic Interpretation of Duality (Section 6.2) Remember McGreasy? (1 of 3) minimize 1 . 84 x QP + 2 . 19 x MD + 1 . 84 x BM + 1 . 44 x FF + 2 . 29 x MC + 0 . 77 x FR + 1 . 29 x SM + 0 . 6 x 1 M + 0 . 72 x OJ subject to Protein: 28 x QP + 24 x + 25 x + 14 x + 31 x + 3 x + 15 x + 9 x 1 M + x OJ 55 Vitamin A: 15 x QP + 15 x + 6 x + 2 x + 8 x + 4 x + 10 x 1 M + 2 x OJ 100 ISyE Lecture #11 4
ISyE Lecture #11 Economic Interpretation of Duality (Section 6.2) Final McDonald’s Model (2 of 3) Vitamin C: 6 x QP + 10 x MD + 2 x BM + 15 x MC + 15 x FR + 4 x 1 M + 120 x OJ 100 Calcium: 30 x QP + 20 x + 25 x + 15 x FF + 15 x + 20 x SM + 30 x 1 M + 2 x OJ 100 Iron: 20 x QP + 20 x + 20 x + 10 x + 8 x + 2 x + 15 x + 2 x OJ 100 ISyE Lecture #11 5

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ISyE Lecture #11 Economic Interpretation of Duality (Section 6.2) Final McDonald’s Model (3 of 3) Calories: 510 x QP + 370 x MD + 500 x BM + 370 x FF + 400 x MC + 220 x FR + 345 x SM + 110 x 1 M + 80 x OJ 2000 Carbs: 34 x QP + 35 x + 42 x + 38 x + 42 x + 26 x + 27 x + 12 x 1 M + 20 x OJ 350 x QP , x , x , x , x , x , x , x 1 M , x OJ 0 ISyE Lecture #11 6
ISyE Lecture #11 Economic Interpretation of Duality (Section 6.2) Get Me Some Bling Wanna Buy Some “Vitamins”? I My meager Assistant Professor Salary will not continue to support my fancy bling lifestyle I Thus, I seek supplementary income by providing “pure” nutrients R on the street R = { Prot, VitA, VitC, Calc, Iron, Cals, Carb } I I need to ﬁgure out the street price for my nutrients. I Can we use Linear Programming to do the trick? ISyE Lecture #11 7

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ISyE Lecture #11 Economic Interpretation of Duality (Section 6.2) Get Me Some Bling Data QP MD BM FF MC FR SM 1M OJ Req’d Cost 1.84 2.19 1.84 1.44 2.29 0.77 1.29 0.6 0.72 Prot 28 24 25 14 31 3 15 9 1 55 VitA 15 15 6 2 8 0 4 10 2 100 VitC 6 10 2 0 15 15 0 4 120 100 Calc 30 20 25 15 15 0 20 30 2 100 Iron 20 20 20 10 8 2 15 0 2 100 Cals 510 370 500 370 400 220 345 110 80 2000 Carb 34 33 42 38 42 26 27 12 20 350 ISyE Lecture #11 8
ISyE Lecture #11 Economic Interpretation of Duality (Section 6.2) Get Me Some Bling Prof. Linderoth’s Bling Model I Let y r be the (per unit) price that I will charge for my “nutrient” r R I My goal: Maximize my per-client proﬁt, if I were able to get someone completely hooked. I They would get all of their daily nutrients from me I This can we written algebraically as max 55 y Prot + 100 y Vita + 100 y VitC + 100 y Calc + 100 y Iron + 2000 y Cals + 350 y Carb ISyE Lecture #11 9

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ISyE Lecture #11 Economic Interpretation of Duality (Section 6.2) Get Me Some Bling What Can I Charge?
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lecture11-handout - ISyE 323 Lecture#11 Prof Je Linderoth...

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