Answer:
$1.5
Explanation:
Given:
Charges per order = $30
Charges per case = $50
1 case = 5 bags of fertilizers
Number of fertilizers bags needed per year = 2000 bags
Annual holding cost, C₀ = 30%
Now,
Annual demand for cases, D =
= ![\frac{\textup{2000}}{\textup{5}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctextup%7B2000%7D%7D%7B%5Ctextup%7B5%7D%7D)
= 400 cases
thus,
Annual unit holding cost per case,
= 30% of $50 i.e $15
Thus,
Economic Order quantity ( EOQ ) =![\sqrt{\frac{2C_oD}{C_h}}](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7B2C_oD%7D%7BC_h%7D%7D)
on substituting the respective values, we get
EOQ =![\sqrt{\frac{2\times30\times400}{15}}](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7B2%5Ctimes30%5Ctimes400%7D%7B15%7D%7D)
or
EOQ = 40
Now,
Annual ordering cost = Ordering cost × Number of orders
= C₀ ×
= $30 × ![\frac{\textup{400}}{\textup{40}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctextup%7B400%7D%7D%7B%5Ctextup%7B40%7D%7D)
= $300
Annual inventory holding cost
= Annual unit inventory holding cost × Average inventory
=
×
= $15 ×
= $300
Now,
Sum of annual ordering and holding cost per case of fertilizer
= $300 + $300
= $600
Therefore,
Annual ordering and holding cost per case of fertiliser
=
= ![\frac{\textup{600}}{\textup{400}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctextup%7B600%7D%7D%7B%5Ctextup%7B400%7D%7D)
= $1.5