Respuesta :
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 = [tex]\frac{\textup{Number of fertilizers bags needed}}{\textup{Number of bags per case}}[/tex]
= [tex]\frac{\textup{2000}}{\textup{5}}[/tex]
= 400 cases
thus,
Annual unit holding cost per case, [tex]C_h[/tex] = 30% of $50 i.e $15
Thus,
Economic Order quantity ( EOQ ) =[tex]\sqrt{\frac{2C_oD}{C_h}}[/tex]
on substituting the respective values, we get
EOQ =[tex]\sqrt{\frac{2\times30\times400}{15}}[/tex]
or
EOQ = 40
Now,
Annual ordering cost = Ordering cost × Number of orders
= C₀ × [tex]\frac{\textup{annual demand}}{\textup{EOQ}}[/tex]
= $30 × [tex]\frac{\textup{400}}{\textup{40}}[/tex]
= $300
Annual inventory holding cost
= Annual unit inventory holding cost × Average inventory
= [tex]C_h[/tex] × [tex]\frac{\textup{EOQ}}{\textup{2}}[/tex]
= $15 × [tex]\frac{\textup{40}}{\textup{2}}[/tex]
= $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
= [tex]\frac{\textup{600}}{\textup{Annual demand}}[/tex]
= [tex]\frac{\textup{600}}{\textup{400}}[/tex]
= $1.5
