27. Suppose you are going on a long trip to your grandmother’s home in Seattle, 3,000 miles away. You have decided to drive your old Ford out there, which gets approximately 18 miles to the gallon when cruising at 70 mph. Because Grandma is an excellent cook and you can stay and eat at her place as long as you want (for free), you want to get to Seattle as economically as possible.

However, you are worried about your fuel consumption rate at high speeds. You also have to balance cost of food, snacks, and sleep to balance against the cost of fuel.

What is the optimum average speed you should use so as to minimize your total trip cost, CT? (2.3)

CT = CG + CFSS CG = n × pg × f (CG = cost of gas)

CFSS = n × pfss × v−1 (CFSS = cost of food, snacks, and sleep)

n: trip length (miles)

pg: gas price, $3.60/gallon pfss: average hourly spending money, $5/hour

(motel, breakfast, snacks, etc., $120 per 24 hours)

v: average Ford velocity (mph)

f=kv, where k is a constant of proportionality and f is the fuel consumption rate in gallons per mile