Facts: Your firm produces and leases vehicles while reimbursing customers for the cost of fuel of these vehicles. Each customer pays you $2,000 a year to operate a vehicle for ten years.  Over the life of a vehicle, the customer drives 20 miles a day for 300 days a year for ten years before scrapping the vehicle (for 60,000 miles in total). The price of gas is now $2 a gallon. The steel vehicle consumes 0.04 gallons per mile (or 25 miles per gallon).   So the firm pays $4,800 for fuel over the course of ten years. Since the cost of producing a vehicle is $10,000, the company’s profit per customer is $2,000*10 - $4,800-$10,000 = $5,200.

You are designing the new version of the vehicle. You could leave the vehicle unchanged and have the company earn $5,200 per customer. Or you could use aluminum. Aluminum reduces weight but increases the cost of making the vehicle by $3 per pound of weight saving. The steel vehicle weighs 3000 lbs. You can only reduce the vehicle weight by 50% using aluminum. Assume that a 50% reduction in vehicle weight leads to a 50% reduction in the number of gallons consumed per mile.

Represent this problem as a decision tree. As a result, probabilities are not involved.   You either choose aluminum and observe the consequences or choose steel and observe the consequences. Also remember that rectangles are only used to represent decisions and ovals are only used to represent uncertainties. It is not used to represent the payoffs at the end of the decision tree.]

How much does your profit change if you use aluminum in the vehicle?:

If gasoline prices increased from $2 to $4 a gallon;

What would be the profit from using steel?

What would be the profit from using aluminum?