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# $Id: chvatal_diet.zpl,v 1.4 2009/09/13 16:15:53 bzfkocht Exp $
#
# From V. Chvatal: Linear Programming
# Chapter 1, Page 3ff.
#
# A diet problem
#
set Food := { "Oatmeal", "Chicken", "Eggs", "Milk", "Pie", "Pork" };
set Nutrients := { "Energy", "Protein", "Calcium" };
set Attr := Nutrients + {"Servings", "Price"};
param needed[Nutrients] := <"Energy"> 2000, <"Protein"> 55, <"Calcium"> 800;
param data[Food * Attr] :=
| "Servings", "Energy", "Protein", "Calcium", "Price" |
|"Oatmeal" | 4 , 110 , 4 , 2 , 3 |
|"Chicken" | 3 , 205 , 32 , 12 , 24 |
|"Eggs" | 2 , 160 , 13 , 54 , 13 |
|"Milk" | 8 , 160 , 8 , 284 , 9 |
|"Pie" | 2 , 420 , 4 , 22 , 20 |
|"Pork" | 2 , 260 , 14 , 80 , 19 |;
# (kcal) (g) (mg) (cents)
var x[<f> in Food] integer >= 0 <= data[f, "Servings"];
minimize cost: sum <f> in Food : data[f, "Price"] * x[f];
subto need :
forall <n> in Nutrients do
sum <f> in Food : data[f, n] * x[f] >= needed[n];
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