Question

For speeds between 40 mph and 65 mph, a diesel truck gets
460x460x miles per gallon when driven at a constant speed of xx
miles per hour. Diesel gasoline costs 4 dollars per gallon. The
driver is paid 22 dollars per hour.

**A)** What is the total cost to have the truck driven
100 miles at a constant speed of 60 miles per hour?

dollars.

**B)** What is the best constant speed to drive the
truck to minimize the total cost to drive it 100 miles?

miles per hour.

**C)** How much money is saved, per 100 miles, by
driving at the the constant speed you found in problem B) instead
of 60 miles per hour?

dollars.

Answer #1

**Solution:**

a)

At speed of 60 miles per hour, the diesel truck will give average of 460/60 = 46/6 miles per gallon Time taken for journey =100/60 hours = 5/3 hours

Total cost = Cost of diesel + Cost of driver

4 ( 600/46 ) + 22 * 5 / 3

$ 88.84

b)

Let the constant speed be x

Time taken = 100/x

Total Cost = Cost of diesel + Cost of driver

4 (100/(460/x)) + 22 * 200/x

400 x / 460 + 2200/x

Taking the derivative

we get

400/460 - 2200 / x^{2} = 0

x = = 50.29

Hence the be. constant speed is 50. 29 mph

C)

Cost with speed of 50.29 will be

400 * 50.29 / 460 + 2200 / 50.29 = 87.47

Money saved = 88.84 - 87.47

= $1.37

Please up vote the solution if it helpful thanks

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