Question

ames runs a car service. He sends a car on a 300-mile trip for a customer. The cost of fuel for each mile traveled depends on the speed in miles per hour, S, and equals pS2, where p is the price of fuel. In addition, he pays his driver $20 per hour. James wants to figure out at what speed the driver should travel to minimize the total cost for the trip. Which expression calculates the total cost?


300
(
20
S
+
p
S
2
)


300
(
20
S
+
p
S
2
)


20
S
300
+
300
p
S
2


300
20
S
+
p
S
2
300

Answer 1

Time = distance/speed = 300/S hours. Driver cost = 20*(300/S) = 6000/S. Fuel cost = (p S^2) * 300 = 300 p S^2.

Total cost C(S) = 6000/S + 300 p S^2 = 300(20/S + p S^2).