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What is the speed at which the cost of the following trip can be minimized: Glynn is considering buying a truck and becoming a professional driver.... |

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Answer:

If Glynn travels at a speed v km/h, the time taken to travel 1500 km is 1500/v. As he pays himself $15/h, the cost incurred would be 22500/v. The running cost of the truck as a function of speed v in km/h is c(v) = 0.85 + 0.0004*v^(3/2) dollars per kilometer.

The total cost of the trip of 1500 km would be C = 22500/v + (0.85+0.0004v^(3/2))*1500

To minimize the cost of the trip, the required speed at which at the truck should be driven is the solution of C' = 0.

C' = (9*v^(5/2)-225000)/(10*v^2)

Solving (9*v^(5/2)-225000) = 0 gives a positive real root of 57.43 km/h

The cost of the trip of 1500 is minimum if the speed at which Glynn travels is 57.43 km/h

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