Find the speed v,in miles per hour,that will minimize costs on a 125-mile delivery trip.The cost per hour for fuel is dollars,and the driver is paid dollars per hour.(Assume there are no costs other than wages and fuel.)
A) 75 mph
B) 125 mph
C) 200 mph
D) 80 mph
E) 40 mph

Question

​Find the speed v,in miles per hour,that will minimize costs on a 125-mile delivery trip.The cost per hour for fuel is  dollars,and the driver is paid  dollars per hour.(Assume there are no costs other than wages and fuel.) ​
A) ​75 mph 
B) ​125 mph 
C) ​200 mph 
D) 80​ mph 
E) ​40 mph

Quizplus · Accepted Answer

The cost to make the delivery depends on the time it takes, and thus the speed at which it is done. We can form a cost function C(v) where v is the speed in miles per hour. Since the trip is 125 miles, the time it takes to make the delivery at a speed of v is given by t = 125/v. 
The cost function, in terms of v, is C(v) = 11(125/v) + 11t = 11(125/v) + 11(125/v) = 250(11/v).
To minimize this function, we want to find the value of v that makes C'(v) = 0. So, differentiating:
C'(v) = - 2750/v^2 = 0
Solving for v, we get v = 80. Therefore, the speed that minimizes the cost of the delivery is 80 mph. Answer: D) 80 mph.

​Find the Speed V,in Miles Per Hour,that Will Minimize Costs

Find the Speed V,in Miles Per Hour,that Will Minimize Costs