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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!!!
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