# Model Linear Program for a car manufacturer

A car manufacturer wants to reduce the weight of a car by at least 400 pounds. Design engineers have identified ten potential design changes that may be used to reduce the vehicle weight, shown in the table below. Changes 4 and 7 are engine block modifications and thus cannot both be selected. Formulate an integer linear programming model to reduce the weight by at least the target amount at the least cost

change 1 2 3 4 5 6 7 8 9 10

Weight

Saved(lbs) 50 75 25 150 60 95 200 40 80 30

Cost($k) 150 350 50 450 90 35 650 75 110 30

https://brainmass.com/math/linear-programming/model-linear-program-car-manufacturer-527055

#### Solution Preview

** Please see the attached file for the complete solution **

Let x_i be the 'indicators' of whether the i-th change will be taken (i.e. x_i = 1 if the i-th change is taken, and x_i =

0 if not). ...

#### Solution Summary

This solution gives a step-by-step explanation on how to model the given problem as an integer program. Some techniques in formulating integer programs are discussed along the solution to provide a better understanding of the topic for the student. The solution is a half-page pdf document.