Question 59969
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!!!