Asimple model for travel costs involves the cost of gasoline and the cost of a driver. specifically, assume that gasoline costs $p/gallon and the vehicle gets g miles per gallon. also, assume that the driver earns $w/hour. complete parts a through g below. a. a plausible function to describe how gas mileage (in mi/gal) varies with speed v is g (v) = v (85−v)/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 formula c (v) =l p/g (v) + l w/v gives the cost of the trip in dollars, where l is the length of the trip and v is the constant speed. show that the dimensions are consistent.
d. let l=400 mi, p=$4/gal, and w=$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 w is decreased from $20/hr. to $15/hr.? explain.