Darius has entered a competition in which he must drive from his home town of Memphis, TN to New Orleans, LA, a distance of approximately 420 miles.

Darius has entered a competition in which he must drive from his home town of Memphis, TN to New Orleans, LA, a distance of approximately 420 miles. If he arrives in 6 hours (an average speed of 70 mph), he will receive a prize of $250. If he arrives in 7 hours (an average speed of 60 mph), he receives $225. One of the competition rules is he must pay for his own gas, and Darius has calculated that he will average 24 mpg at 70 mph and 30 mpg at 60 mph. To maximize his winnings (prize money minus the cost of gas), at what speed should Darius drive if the price of gas is $4 per gallon? What if the price of gas is $5 per gallon? At what gas price would Darius be indifferent to arriving in either 6 or 7 hours if he wants to maximize his winnings? Other than maximizing winnings, are there any other considerations Darius should take into account when deciding on how fast to drive? Explain