Answer :
Solution :
Given :
The annual demand, [tex]$D=5000$[/tex] units
Ordering cost, [tex]$S=\$30$[/tex]
Carrying cost, [tex]$H=\$50$[/tex]
Lead time, L = 10 days
Number of days per year = 250 days
So, average demand is d = [tex]$\frac{D}{250}$[/tex] days
= [tex]$\frac{5000}{250}$[/tex] = 20 units
a). The economic order quantity, Q = [tex]$\sqrt{\frac{2DS}{H}}$[/tex]
[tex]$=\sqrt{\frac{2\times 5000 \times 30}{50}}$[/tex]
= 77 units
b). Average inventory = [tex]$\frac{Q}{2}$[/tex]
[tex]$=\frac{77}{2}$[/tex]
≈ 39 units
c). Number of orders per year = [tex]$\frac{D}{Q}$[/tex]
[tex]$=\frac{5000}{77}$[/tex]
= 65 units
d). Time between orders = [tex]$\frac{Q}{D}$[/tex] x number of days per year
[tex]$=\frac{77}{5000} \times250$[/tex]
= 3.85
e). Annual ordering cost = [tex]$\frac{D}{Q} \times S$[/tex]
[tex]$=\frac{5000}{77} \times 30$[/tex]
= $ 1948.05
Annual carrying cost = [tex]$\frac{Q}{2} \times H$[/tex]
[tex]$=\frac{77}{2} \times 50$[/tex]
= $ 1925
Total annual cost of inventory = $ 1948.05 + $ 1925
= $ 3873.05
f). Reorder point = [tex]$d \times L$[/tex]
[tex]$=20 \times 10$[/tex]
[tex]$=200$[/tex] units