Question

10. An electric scooter manufacturer estimates that the cost C in dollars) of producing x

scooters is given by C(x) = 600+ 0.05x + 0.0002x%. Find the production level, to the nearest
unit, that will minimize the average cost Č(x) per unit.
A. 1733 scooters
B.
1250 scooters
C. 600 scooters
D.
1500 scooters

Answer 1

A. 1733 scooters

Explanation:

To get x for minimum value of C bar, set derivative = 0

We Find our x.

C(x) = 600+ 0.05x + 0.0002x^2

We need average cos per unit

So divide by x both sides

C(x) / x = 600/x + 0.05x + 0.0002x

c(x)/c = Ç(x)

Therefore, Ç(x) = 600/x + 0.05x + 0.0002x

Now differentiate both side with x

dÇ(x)/dx = 600/x^2 + 0 + 0.0002

To find x for minimum Ç(x)

Set dÇ(x)/dx = 0 => -600/x^2 + 0.0002 = 0

=> x^2 = 600/0.0002

x^2 =3000000

x = √3000000

x = 1732.05

x = 1733