A company is planning to send a shipment over a distance of 300 300 miles. The truck consumes diesel at a rate described by the function d ( v ) = v ( 90 − v ) 70 d\left(v\right)=\frac{v\left(90-v\right)}{70} , where d d is the diesel efficiency in mi/gal and v v is the speed in mph. The diesel costs $ 3 \$3 per gallon, and the driver's wage is $ 25 \$25 per hour. Should the speed that minimizes the cost be increased or decreased if the distance is increased from 300 300 miles to 400 400 miles? Justify your answer.

Table of contents

5. Graphical Applications of Derivatives

Applied Optimization

5. Graphical Applications of Derivatives

Applied Optimization: Study with Video Lessons, Practice Problems & Examples

14PRACTICE PROBLEM

ANSWERS OPTIONS

It should be increased because a longer distance means a larger wage for the driver.

It should be decreased because at a longer distance, the fuel efficiency is higher at lower speeds.

It should be increased because a longer distance means a greater fuel efficiency, which improves at higher speeds.

It should neither be increased nor decreased because the speed that minimizes the cost remains the same regardless of the distance.