The cost of operating a large ship (co) varies as the square of its velocity (v); specically, co = knv2, where n is the trip
length in miles and k is a constant of proportionality. it is known that at 12 miles/hour, the average cost of operation is
$100 per mile. the owner of the ship wants to minimize the cost of operation, but it must be balanced against the cost of
the perishable cargo (cc), which the customer has set at $1,500 per hour. at what velocity should the trip be planned to minimize the total cost (ct), which is the sum of the cost of operating the ship and the cost of perishable cargo? (problem)
problem
a group of enterprising engineering students has developed a process for extracting combustible methane gas from cow manure (don't worry the exhaust is odorless). with a specially adapted internal combustion engine, the students claim that
an automobile can be propelled 15 miles per day from the "cow gas" produced by a single cow. their experimental car can
travel 60 miles per day for an estimated cost of s5 (this is the allocated cost of the methane process equipment—the cow manure is essentially free).
a. how many cows would it take to fuel 1,000,000 miles of annual driving by a eet of cars? what is the annual cost?
b. how does your answer to part (a) compare to a gasoline-fueled car averaging 30 miles per gallon when the cost of
gasoline is $3.00 per gallon?