Robert has entered a competition in which he must drive from his home town of Paris to London, a distance of approximately 450 km. If he arrives in 5 hours (an average speed of 90 km/h), he will receive a prize of €300. If he arrives in 6 hours (an average speed of 75 km/h), he receives €270.
One of the competition rules is he must pay for his own gasoline, and Robert has calculated that he will average 20 km per liter at 90 km/h and 25 km per liter at 75 km/h.
To maximize his winnings (prize money minus the cost of gasoline), at what speed should Robert drive if the price of gasoline is €3.00 per liter? What if the price of gasoline is €4.00 per liter? At what gasoline price would Robert be indifferent to arriving in either 5 hours or 6 hours if he wants to maximize his winnings? Other than maximizing winnings, are there any other considerations Robert should take into account when deciding on how fast to drive? Briefly explain.