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Mixed integer programming

The Wiethoff Company has a contract to produce 10000 garden hoses for a customer. Wiethoff has 4 different machines that can produce this kind of hose. Because these machines are from different manufacturers and use differing technologies, their specifications are not the same.

Machine Fixed cost to set up production Capacity
Variable cost per hose
1 750 1.25 6000
2 500 1.50 7500
3 1000 1.00 4000
4 300 2.00 5000

The company wants to minimize total cost. Give the objective function

Solution Preview


There are two types of variables in this problem: 1. Production variables (continous) and selection variables (binary). These binary variables are for fixed cost.

Let x1: Quantity produced on machine 1
x2: Quantity produced on machine ...

Solution Summary

Objective function for minimizing total cost is given in the solution.