Engineering Board Exam Reviewer · Optimization (Maxima and Minima) · medium
The fuel cost of a ship is P0.002v3 per hour, where v is the speed in km/h, and other costs total P100 per hour. Find the speed that minimizes the total cost per kilometer.
- 50 km/h
- 25 km/h
- 14.62 km/h
- 29.24 km/h
Answer
D. 29.24 km/h
Solution
Cost per km: C(v)=0.002v3+100/v=0.002v2+100/v. C'(v)=0.004v-100/v2=0 v3=25000 v 29.24 km/h.
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