SOLUTION: My homework is needed tommorow and have no idea of working through it . please assist or even a hint would help ... Power climbers Bi- motors Ltd orders and sells mountain

Question 59969: My homework is needed tommorow and have no idea of working through it .
please assist or even a hint would help ...

Power climbers Bi- motors Ltd orders and sells mountain climbers bikers. The company�s cost accountant has examined cost data and established a cost function which expresses the annual cost (C) in K $ of purchasing, owning and maintaining inventory as a function of size of each order (q) it places for the bikes. The function is specifically of the form:
C = 4860/q + 15q + 250,000
Determine the order that minimizes annual inventory list and the minimum average inventory cost per unit.

Answer by uma(370) (Show Source): You can put this solution on YOUR website!
The cost function C = 4860/q + 15q + 250000
Differentiate this with respect to q
==> dC/dq = -4860/(q^2) + 15 --------------(1)
Equate dC/dq = 0
==> -4860/(q^2) + 15 = 0
==> -4860 + 15q^2 = 0 [multiplying by q^2 throughout]
==> 15q^2 = 4860 [Adding 4860 to both the sides]
==> 15q^2 /15 = 4860/15
==> q^2 = 324
==> q = 18 [taking square root]
Differentiating (1) with respect to q,
d^2C/dq^2 = 4860/q^3
Plugging in q = 18 in the above,
d^2C/dq^2 = 4860/(18^3) which is positive
So the cost is minimum for q = 18
Thus the order that minimises the annual inventory = 18
Minimum average inventory cost = 4860/q + 15q + 250000 at q = 18
= 4860/18 + 15(18) + 250000
= 270 + 270 + 250000
= 250540
This is the cost for 18 units.
So cost per unit = 250540/18
= 13919$
Good Luck!!!

RELATED QUESTIONS
A swimming pool contains 40000 gallons of water. How many gallons of chlorine must be (answered by checkley71)

Good Afternoon, Sam here. I am having a terrible time trying to solve this story or word... (answered by edjones)

'In rectangle ABCD, two consecutive sides and the diagonal are all consecutive integers.... (answered by richwmiller)

How do you simplify fractions? Please help me. I am home taught and my parents have no... (answered by tutorcecilia)

I am trying to help my son with his math homework and have no idea what the answer is or... (answered by ptaylor)

I used quarters to pay a loan from Brad. If I had paid using nickels, I would have needed (answered by MathTherapy)

i need help with prime factorization. i have no idea what it is and i have a homework... (answered by elima)

Took a test two days ago, did great, trying to make corrections on this ONE problem. Can... (answered by DrBeeee)

a lab needs to make 100 gallons of an 18% acis solution by mixing a 12% acid solition... (answered by josmiceli)