Manuals/calci/Exampleslp

Linear Programming Examples in z3

DESCRIPTION

• Basic Linear Programming examples in z3.
  
• Reflecting different domains like Engineering, Statistics, Medicine, etc.
• Testing how we can make better solutions to the standard problems compared to other software.
  
  

Examples

ExampleS1: Chocolate Problem
Shannon's Chocolates produces semisweet chocolate chips and milk chocolate chips at its plants in Wichita, KS and Moore, OK. The Wichita plant produces 3000 pounds of semisweet chips and 2000 pounds of milk chocolate chips each day at a cost of $1000, while the Moore plant produces 1000 pounds of semisweet chips and 6000 pounds of milk chocolate chips each day at a cost of $1500. Shannon has an order from Food Box Supermarkets for at least 30,000 pounds of semisweet chips and 60,000 pounds of milk chocolate chips. How should Shannon schedule its production so that it can fill the order at minimum cost? What is the minimum cost?

z3 code: Chocolate Problem

var solver = require('javascript-lp-solver'),
	results,
    model = {
    "name": "Chocolate Problem",
    "optimize": "cost",
    "opType": "min",
    "constraints": {
        "semisweet": {
            "min": 30000
        },
        "milk chocolate": {
            "min": 60000
        }
    },
    "variables": {
        "Kansas": {
            "semisweet": 3000,
            "milk chocolate": 2000,
            "cost": 1000
        },
        "Oklahoma": {
            "semisweet": 1000,
            "milk chocolate": 6000,
            "cost": 1500
        }
    }
};
    
console.log(solver.Solve(model));

Solution:

{ feasible: true,
  result: 18750,
  bounded: true,
  Kansas: 7.5,
  Oklahoma: 7.5 }