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?
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?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Thomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSON
Calculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. Freeman
Calculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning