Brenda drives an 18 wheeler. she plans to buy her own truck. Her research indicates that the expected running costs, C, in dollars, per 100 km, are given by C(v)=0.9 +0.0016v square, where v is the speed, in kilometers per hour. Brenda's first trip will be 1500 km, round trip. she plans to pay herself $30/h. determine the speed that will minimize Brend's cost for the trip

Question

Brenda drives an 18 wheeler.   she plans to buy her own truck. Her research indicates that the expected running costs, C, in dollars, per 100 km, are given by C(v)=0.9 +0.0016v square, where v is the speed, in kilometers per hour.   Brenda's first trip will be 1500 km, round trip. she plans to pay herself $30/h.  determine the speed that will minimize Brend's cost for the trip

anonymous · Answer

x(0.0016x^2+0.9)/100=30 
x=121.790 
Total cost of trip (1500/x)*(x(0.0016x^2+0.9/100)=15(0.0016x^2+0.9)
 x is the speed in km/hr, so that cost is 30 $/hr. Any speed less than that would result in lower $/hr as well as lower cost of the trip.

anonymous · Answer

The answer in the textbook says 97.9 km/hr

anonymous · Answer

The answer in the textbook says 97.9 km/hr