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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4.4 - Problem 57e
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4.4 - Problem 57e

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# Travel costs A simple model for travel costs involves the

ISBN: 9780321570567 2

## Solution for problem 57E Chapter 4.4

Calculus: Early Transcendentals | 1st Edition

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Problem 57E

Travel costs A simple model for travel costs involves the cost of gasoline and the cost of a driver. Specifically, assume that gasoline costs $p per gallon and the vehicle gets ?g? miles per gallon. Also, assume that the driver earns$w/hour. a. A plausible function to describe how gas mileage (in mi/gal) varies with speed is g?(???)= ???(85??)/60. Evaluate g(0), g(40), and ?g?(60) and explain why these values are reasonable. b. At what speed does the gas mileage function have its maximum? c. Explain why the cost of a trip of length ?L? miles is ?C?(?v?)= ?Lp/g?(???)+ ?Lw/??. d.Let ?L? =400 mi, ?p? =$4/gal, and to =$20/hr. At what (constant) speed should the vehicle be driven to minimize the cost of the trip? e. Should the optimal speed be increased or decreased [compared with part (d)] if ?L is increased from 400 mi to 500 mi? Explain. f. Should the optimal speed be increased or decreased [compared with part (d)] if ?p is increased from $4/gal to$4.20/gal? Explain. g. Should the optimal speed be increased or decreased [compared with part (d)] if ?to is decreased from $20/hr to$15/hr? Explain.

Step-by-Step Solution:

Solution Step 1 Consider that a simple model for travel costs involves the cost of gasoline and the cost of driver. It is assumed that the gasoline costs per gallon and the vehicle gets miles per gallon. Also, it is assumed that the driver earns per gallon.

Step 2 of 7

Step 3 of 7

##### ISBN: 9780321570567

The full step-by-step solution to problem: 57E from chapter: 4.4 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Since the solution to 57E from 4.4 chapter was answered, more than 1868 students have viewed the full step-by-step answer. The answer to “Travel costs A simple model for travel costs involves the cost of gasoline and the cost of a driver. Specifically, assume that gasoline costs $p per gallon and the vehicle gets ?g? miles per gallon. Also, assume that the driver earns$w/hour. a. A plausible function to describe how gas mileage (in mi/gal) varies with speed is g?(???)= ???(85??)/60. Evaluate g(0), g(40), and ?g?(60) and explain why these values are reasonable. b. At what speed does the gas mileage function have its maximum? c. Explain why the cost of a trip of length ?L? miles is ?C?(?v?)= ?Lp/g?(???)+ ?Lw/??. d.Let ?L? =400 mi, ?p? =$4/gal, and to =$20/hr. At what (constant) speed should the vehicle be driven to minimize the cost of the trip? e. Should the optimal speed be increased or decreased [compared with part (d)] if ?L is increased from 400 mi to 500 mi? Explain. f. Should the optimal speed be increased or decreased [compared with part (d)] if ?p is increased from $4/gal to$4.20/gal? Explain. g. Should the optimal speed be increased or decreased [compared with part (d)] if ?to is decreased from $20/hr to$15/hr? Explain.” is broken down into a number of easy to follow steps, and 193 words. This full solution covers the following key subjects: speed, increased, explain, should, cost. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567.

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