The ordering and transportation cost C for components used in a manufacturing process is approximated by the function below, where C is measured in thousands of dollars and x is the order size in hundreds.

Question

C(x) = 12((1/x)+((x)/(x+3)))

(a) Verify that C(2) = C(15).
C(2) = 54/5


C(15) = 54/5



(b) According to Rolle's Theorem, the rate of change of the cost must by 0 for some order size in the interval (2, 15). Find that order size. (Round your answer to the nearest whole number.)

What is the answer to part b? I found the the derivative of C(x) and set it equal to zero and got approximately 4, but that isn't the right answer. Please help!!!

Answer 1

Rolle's Theorem says that since C(2)=C(15), there is some value 2<c<15 such that C'(c) = 0.

dC/dx = 12(2x^2-6x-9)/(x(x+3))^2
dC/dx=0 when 2x^2-6x-9=0, or
x = 3/2 (1±√3)
or, x = -1.1, 4.1

So, your answer of 4 is correct. The graph at

http://www.wolframalpha.com/input/?i=12%28%281%2Fx%29%2B%28%28x%29%2F%28x%2B3%29%29%29+

shows the minimum in the desired interval, where C' is zero.