Optimizing Fuel Cost for a Truck on a 400 Mile Trip

AI Thread Summary
The discussion revolves around calculating the fuel cost for a truck on a 400-mile trip, using the fuel consumption function G(x) defined as G(x) = (1/32)(64/x + x/50). Participants seek to derive the cost function C(x) based on this fuel consumption, with fuel priced at $1.60 per gallon. There is confusion regarding the variable x, which is clarified to represent speed in miles per hour, not distance. The main goal is to find both the cost function and the optimal speed for minimizing costs during the trip. The thread highlights a need for assistance in solving these mathematical problems.
ziddy83
Messages
87
Reaction score
0
I was wondering if anyone can help me on this problem...

A truck burns fuel at the rate of G(x) gallons per mile. Where

G(x) = \frac {1} {32} \left(\frac {64}{x} + \frac {x}{50} \right)

a. Find the cost function C(x) if the truck takes a 400 mile trip. Assume that the cost of fuel is $1.60 per gallon.

b. What is the speed that will produce minimum cost on this trip?

So...if anyone can help me with this...Please..please do so, I would be very very appreciative. Thanks
 
Physics news on Phys.org
What does x represent?


At first I thought it was the distance which makes (a) easy but then (b) makes no sense. Is x the speed? No, that way (a) makes no sense!
 
oh sorry...x represents miles per hour
 
How can i determine the cost function? Anyone?
 
nobody can help?
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

MHB Optimizing Truck Speed and Freight Load for Cost Efficiency on Interstate Travel
Replies
10
Views
3K
How much does it cost to run 300 school buses for 22 days?
Replies
6
Views
5K
Solve Calc Homework: Optimization Problems | Help with v, Cost & Wages
Replies
3
Views
2K
Optimization - help needed setting up a system of equations?
Replies
2
Views
6K
NS Derailment, East Palestine, Ohio - 3 Feb, 2023 - Engineering Aspect
Replies
9
Views
3K
Derivative of Cost Function with Respect to Output Layer Weight
Replies
31
Views
3K
Second Law of Thermodynamics - Entropy
Replies
1
Views
4K
Find function with given boundary conditions
Replies
1
Views
1K
What Speed Minimizes Total Cost for a 1000-km Truck Journey?
Replies
9
Views
5K
MHB Which Catering Service Maximizes Charity Profit for a Business Banquet?
Replies
2
Views
6K

Hot Threads

Recent Insights

Back
Top