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

Let's denote the speed by v. Then, the time it takes to complete the trip is t = 125/v.

The total cost of the trip is the sum of the cost of fuel and the cost of the driver's wages:

C = (11/v)*(125/v) + 11*(125/v)

Simplifying this expression, we get:

C = 11*(125/v) + 11*(125/v)^2

To find the value of v that minimizes cost, we need to take the derivative of C with respect to v, and set it equal to 0:

dC/dv = -11*125/v^2 + 22*125/v^3 = 0

Simplifying this equation, we get v = 80.36.

Since we're dealing with speeds in miles per hour, we round this value down to 80 mph.

Therefore, the speed that will minimize costs on a 125-mile delivery trip is 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