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Question 1 A truck is to travel 1000 kilometres at a constant speed of v km/h. When travelling at v km/h, the truck 1² consumes fuel at the rate of 6+- litres per hour. The truck company pays 50 cents/litre for fuel and 50 pays each of the two drivers $20 per hour whilst the truck is travelling. (a) Let the total cost of fuel and the drivers' wages for the trip be C dollars. Show that C = 10v+- 43000 V (b) The truck must take no longer than 12 hours to complete the trip, and speed limits require that v≤100. At what speed v should the truck travel to minimise the cost C?

Question 1 A truck is to travel 1000 kilometres at a constant speed of v km/h. When travelling at v km/h, the truck 1² consumes fuel at the rate of 6+- litres per hour. The truck company pays 50 cents/litre for fuel and 50 pays each of the two drivers $20 per hour whilst the truck is travelling. (a) Let the total cost of fuel and the drivers' wages for the trip be C dollars. Show that C = 10v+- 43000 V (b) The truck must take no longer than 12 hours to complete the trip, and speed limits require that v≤100. At what speed v should the truck travel to minimise the cost C?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question 1 A truck is to travel 1000 kilometres at a constant speed of v km/h. When travelling at v km/h, the truck consumes fuel at the rate of 6+ (6+ litres per hour. The truck company pays 50 cents/litre for fuel and each of the two drivers $20 per hour whilst the truck is travelling. 50 pays (a) Let the total cost of fuel and the drivers' wages for the trip be C dollars. Show that C = 10v+ 43000 V (b) The truck must take no longer than 12 hours to complete the trip, and speed limits require that v<100. At what speed v should the truck travel to minimise the cost C?
Transcribed Image Text:Question 1 A truck is to travel 1000 kilometres at a constant speed of v km/h. When travelling at v km/h, the truck consumes fuel at the rate of 6+ (6+ litres per hour. The truck company pays 50 cents/litre for fuel and each of the two drivers $20 per hour whilst the truck is travelling. 50 pays (a) Let the total cost of fuel and the drivers' wages for the trip be C dollars. Show that C = 10v+ 43000 V (b) The truck must take no longer than 12 hours to complete the trip, and speed limits require that v<100. At what speed v should the truck travel to minimise the cost C?
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