Here are some facts about semi-trucks and a trip between Chicago and New Orleans.
(a) The trip is 750 miles.
(b) Running at 50 mph, the truck gets around 4 miles per gallon.
(c) For each mph increase in speed, the truck losses 1/10 of a mile per gallon in mileage.
(d) The driver team gets \$27 per hour.
(e) Keeping the truck on the road costs 15 dollars per hour over and above the cost of fuel.
(f) Diesel fuel costs \$3.90 per gallon.
- Write a function, C(x), for the total cost of driving the truck from Chicago to New Orleans in terms of the constant speed x.
- At what (constant) speed should the truck be driven to minimize the cost of the trip? Use calculus to minimize costs.
Progress
I know that the constraint is $xh=750$ and I know that it something$+27h+(15h/3.90)$ but I don't know how to use the mpg to my equation…
Best Answer
The total cost should be: (cost for driver team) + (cost of fuel) + (cost to keep the truck on the road) The cost of the driver team is 27h, as you have written. The cost to keep the truck on the road is 15h. The "over and above the cost of fuel" doesn't mean that you should divide this by the cost of fuel per gallon, it means "in addition to fuel cost". So you need to figure out the cost of fuel, which is where you will use the mpg.