Solve Calc Homework: Optimization Problems | Help with v, Cost & Wages

[prinzessin04]

a friend in my calc class today told me you guys are amazing at answering his questions... i have some questions on a few optimization problems we have for homework

#1. Suppose that the cost of operating a truck in Mexico is 53+.31v cents per mile when the truck runs at a steady speed of v miles per hour. The top speed of the truck is 100 mph. Assume that the driver is paid 9 dollars per hour to drive the truck, and he is to begin a 2800 mile trip.

Write the cost of operating the truck in dollars, as a function of the speed v, for the planned trip:

Write the cost of driver's wages in dollars, as a function of the speed v, for the planned trip:

The total cost of the planned trip, as a function of the speed v, is the sum of the first two costs. Find the most economic speed for the planned trip, i.e., the speed that minimize the total cost is v=

so i found the derivative of the speed (f'(v)=.31)but I'm not sure if i need that since it seems like i need to make a whole new equation with the number they gave me... where do i go from here?? please help me

 

[turin]

... i found the derivative of the speed (f'(v)=.31)

No, you didn't (according to the parenthetical); you found the derivative of the cost of operating the truck per mile wrt veloctiy.

... it seems like i need to make a whole new equation ...

Yes. Read this:

The total cost of the planned trip, as a function of the speed v, is the sum of the first two costs.

Optimization means minimization in this case. You want to minimize total cost, which must include the cost required to pay the driver. This cost can be expressed as a function of velocity. Then you add it to the one for operating the truck. Once you have done this, differentiate and minimize.

 

[Doc Al]

You found the derivative of something, but it's not the cost function--and it's not the speed.

Follow the directions! The cost function has two pieces, and they tell you enough info to figure out each piece. So figure out the pieces, add them to create the cost function. Then find the minimum of that function.

I'll do the first piece for you: the cost of operating the truck for a trip of 2800 miles, in dollars, is: 28*(53+.31v)

Note: turin beat me to it!

 

[prinzessin04]

thanks i think i got part b) and c) now! you guys are great