Question

Aki’s bicycle designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by C(x)= 0.1x^2-0.3x+5.634, where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle?

Answer 1

C(x) = 0.1*x^2-0.3*x + 5.634
Differentiate with respect to x
C'(x) = d/dx(0.1*x^2-0.3*x + 5.634)
= 0.2*x-0.3

To find endpoints, we need to equate this to 0
So,
0.2*x-0.3 = 0
x = 1.50

Lets find double differentiation
C'(x) = 0.2*x-0.3
Differentiate with respect to x
C''(x) = d/dx(0.2*x-0.3)
= 0.2

Lets find value of double differentiation at all endpoints
C''(x) = 0.2
C''(1.5) = 0.2
= 0.2
Since this is positive, x = 1.5 is minima

So, x = 1.50
that 1.50 hundred bicycle
= 1.50*100
= 150
Answer: 150