The cost of fuel per km for a truck travelling at a speed v[km/h] is given by C(v)=v/100+25/v. (a) What speed result in the lowest fuel cost per km (b) Assume the driver is paid $40/h. What speed would give the lowest cost, including wage for 1000Km?

1 Answer
Feb 10, 2018

(a) 50 km/hr (b) sqrt6500 ~~80 km/hr

Explanation:

(a) We seek to find v that will minimize C(v) = v/100+25/v (with v > 0

C'(v) = 1/100 -25/v^2 and

1/100 -25/v^2 = 0 at v=50 km.

Use either the first or second derivative test to verify that C(50) is a minimum.

(b)

For a trip of 1,000 km we will have

Fuel cost = 1000(v/100+25/v).

The time required is 1000/v hr, so the driver cost is

40 (1000/v).

The total cost is

T(v) = 1000(v/100+25/v) + 40 (1000/v)

= 10v +65000/v

We seek v to mimimize T.

T'(v) = 10-65000/v^2 = 0 at

v^2= 6500