You are the owner of a delivery company with one truck. The trucks fuel economy is 1200/x miles per gallon when driving at x miles per hour (where 80 >= x <= 110). The price of fuel is $1 per gallon. You pay the truck driver $8 per hour.

Question

If a delivery 100 miles away is planned, at what speed between 80 and 110 mph should the truck to drive to minimize the cost of the trip?

Can someone explain step by step how to do this? I have no idea how to approach it.
Thanks in advance!

Answer 1

cost= 8t+fuel cost.

fuel cost= cost per gallon*gallons needed
= 1*100/(1200/x)

But t= 100miles/x

cost= 8*100/x + x/12 check that

dcost/dx=0=-800/x^2 + 1/12
x^2=9600
x= you do it.

Answer 2

how do you check?