ISE203 / IE251 - Optimization I - Linear Models
2015-2016 Fall Term CASE STUDY
Due Date: 30.12.2015 17:00 (no late submissions will be accepted)
Submit your OPL files to:
BIG MAC ATTACK: Eating at McDonald’s
Ø More than 43 million people in 119 countries eat at McDonalds every day
Ø Is it possible to eat healthy at McDonald’s?
· Can you find a daily diet that is
1. Entirely from McDonald’s menu, and
2. Nutritionally complete?
· If so, which such diet has minimum cost? Answer all the questions in page 3.
US National Research Council’s Recommended Daily Diet:
1) At least 100 percent of the US RDA (Recommended Daily Allowances) of Vitamin A, C, B1, B2, Niacin, Calcium and Iron nutrients.
2) Sodium at most 2400 mgs.
3) At least 1400 calories, at most 2000 calories.
4) Protein at most 70 grs, fat at most 50 grs.
5) At most 20% of calories should come from fat. Each gram of fat contains 9 calories.
Nutritional Value of Menu Items
% US Recommended Daily Allowances (RDA)
Menu Item / Vit.A / Vit.
C / Vit.
B1 / Vit.
B2 / Niacin / Calc. / Iron
H / 4 / 4 / 20 / 10 / 20 / 10 / 15
BM / 6 / 2 / 30 / 25 / 35 / 25 / 20
FF / 0 / 15 / 10 / 0 / 10 / 0 / 2
CN / 0 / 0 / 8 / 8 / 40 / 0 / 6
CS / 100 / 35 / 20 / 15 / 20 / 15 / 8
EM / 10 / 0 / 30 / 20 / 20 / 25 / 15
W / 20 / 20 / 20 / 20 / 20 / 2 / 20
VYC / 2 / 0 / 2 / 10 / 2 / 10 / 0
M / 10 / 4 / 8 / 30 / 0 / 30 / 0
OJ / 0 / 120 / 10 / 0 / 0 / 0 / 0
Questions
1-) Formulate an LP model to minimize the cost of US Research Council’s recommended daily diet. Clearly define all decision variables.
2-) Find the optimal amount of each menu item to be consumed, from your model’s solution in part 1. (Use OPL. Attach the OPL file to your submission)
3-) Answer the following questions:
a-) How much should the price of BM be in order to be part of the diet?
b-) How much should the price of CS be in order to be part of the diet?
c-) If you could do with 100 less calories, how much would your cost go down?