Suppose that the cost of operating a truck in Mexico is 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 10 dollars per hour to drive the truck, and he is to begin a 1600 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=
You left out a formula for cents per mile in terms of speed, v. Operating cost should increase with speed, since mpg goes down. You need that formula to solve the problem.
To calculate the cost of operating the truck in dollars for the planned trip, we need to determine the total number of miles the truck will cover and multiply it by the operating cost per mile.
The total number of miles for the planned trip is 1600 miles.
Since the operating cost is given in cents per mile, we need to convert it to dollars per mile by dividing it by 100.
Let's denote the operating cost per mile as c, and the speed of the truck as v.
The cost of operating the truck in dollars, as a function of the speed v, for the planned trip is given by:
Cost of Operation = (c/100) * 1600
Next, let's calculate the cost of the driver's wages for the planned trip.
We know that the driver is paid 10 dollars per hour, and the trip will take a certain amount of time depending on the speed v. We can calculate the time it takes to complete the trip by dividing the total distance by the speed.
The time to complete the trip, in hours, is given by:
Time = Distance / Speed
Time = 1600 / v
The cost of the driver's wages, as a function of the speed v, for the planned trip is given by:
Cost of Driver's Wages = 10 * Time
Cost of Driver's Wages = 10 * (1600 / v)
Finally, we can calculate the total cost of the planned trip by summing up the cost of operation and the cost of driver's wages:
Total Cost = Cost of Operation + Cost of Driver's Wages
Total Cost = (c/100) * 1600 + 10 * (1600 / v)
To find the most economic speed for the planned trip, we need to find the value of v that minimizes the total cost. Differentiating the total cost function with respect to v and setting it to zero, we can find the value of v that minimizes the cost.
I'm sorry, but without knowing the specific value of the operating cost per mile (c), we cannot determine the most economic speed for the planned trip.