An automobile manufacturer is considering mechanical design changes in one of its top selling cars to reduce the weight of the car by at least 400 pounds to improve its fuel efficiency. Design engineers have identified 10 changes that could be made in the car to make it lighter (for example, using composite body pieces rather than metal). The weight saved by each design change and the estimated costs of implementing each change are summarized in the following table.
Design 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 (in $1,000's) $150 $350 $50 $450 $90 $35 $650 $75 $110 $30
Alternative ways of modifying the engine block and, therefore, only one of these options could be selected. The company wants to determine which changes to make in order to reduce the total weight of the car by at least 400 pounds in the least costly manner.
A. Formulate the IP for this problem.
B. What is the optimal solution from your model?