Travel costs A simple model for travel costs involves the cost of gasoline and the cost of a driver. Specifically, assume that gasoline costs $p per gallon and the vehicle gets ?g? miles per gallon. Also, assume that the driver earns $w/hour. a. A plausible function to describe how gas mileage (in mi/gal) varies with speed is g?(???)= ???(85??)/60. Evaluate g(0), g(40), and ?g?(60) and explain why these values are reasonable. b. At what speed does the gas mileage function have its maximum? c. Explain why the cost of a trip of length ?L? miles is ?C?(?v?)= ?Lp/g?(???)+ ?Lw/??. d.Let ?L? =400 mi, ?p? =$4/gal, and to = $20/hr. At what (constant) speed should the vehicle be driven to minimize the cost of the trip? e. Should the optimal speed be increased or decreased [compared with part (d)] if ?L is increased from 400 mi to 500 mi? Explain. f. Should the optimal speed be increased or decreased [compared with part (d)] if ?p is increased from $4/gal to $4.20/gal? Explain. g. Should the optimal speed be increased or decreased [compared with part (d)] if ?to is decreased from $20/hr to $15/hr? Explain.

Solution Step 1 Consider that a simple model for travel costs involves the cost of gasoline and the cost of driver. It is assumed that the gasoline costs per gallon and the vehicle gets miles per gallon. Also, it is assumed that the driver earns per gallon.