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 $C = \frac { v ^ { 2 } } { 800 }$ dollars, and the driver is paid $W = \$ 8$ dollars per hour. (Assume there are no costs other than wages and fuel.)
A)675 mph
B)125 mph
C)800 mph
D)80 mph
E)40 mph

Question

Quizplus · Accepted Answer

To minimize costs, we need to minimize the total cost function, which is the sum of fuel cost and wage cost. The total cost per hour is $ \frac{v^2}{800} + 8 $. The time taken for the trip is $ \frac{125}{v} $ hours. The total cost for the trip is $ \left( \frac{v^2}{800} + 8 \right) \times \frac{125}{v} $. Simplifying and differentiating this expression with respect to $ v $, and setting the derivative to zero, we find that the speed $ v $ that minimizes the cost is 80 mph.

Find the Speed V, in Miles Per Hour, That Will C=v2800C = \frac { v ^ { 2 } } { 800 }C=800v2​

Find the Speed V, in Miles Per Hour, That Will $C = \frac { v ^ { 2 } } { 800 }$