Answer:
x = 55 Miles per hour
Explanation:
Length of trip, L = 300 miles
If "x" is the velocity in miles per hour, time t taken to complete the trip = Length / velocity
t = L / x
There are two components of cost:
The cost per hour for fuel is C dollars, and the driver is paid W dollars per hour.
Hence the cost for the entire trip = The cost per hour for fuel x total number of hours + Hourly cost driver x total number of hours = C*t + W*t
C = 2 + (1/600)*x², W = 13.00 and t = 300 / x
Hence our total cost of the trip,
TC(x) = (2 + (1/600)*x²)*(300 / x) + 13*(300 / x)
TC(x) = (4500 / x) + (x / 2)
In order to minimise this total cost, we need to differentiate this with respect to x and equate it to zero:
TC’(x) = ((4500 / x) + (x / 2))’ = 0
(- 4500 / x²) + (1 / 2) = 0
this equation gives x₁ = - 94.868 and x₂ = 94.868
as we know that 35 ≤ x ≤ 55
we can say that x = 55 Miles per hour (which is the maximum value)
