Answer:
EOQ = 1,095 units
Reorder point: 240 units (at this point the company must do an order to about stock-out)
Cycle time: 33 days (each order last 33 days)
Inventory cost:
ordering cost: 12,000 / 1,095.44 x $25 per order = $ 273.86
holding cost: 1,095.44 /2 x 0.5 = $273.86
Total: 273.86 + 273.86 = $547.52
Explanation:
Economic Order Quantity:
![Q_{opt} = \sqrt{\frac{2DS}{H}}](https://tex.z-dn.net/?f=Q_%7Bopt%7D%20%3D%20%5Csqrt%7B%5Cfrac%7B2DS%7D%7BH%7D%7D)
D = annual demand =12,000
S= setup cost = ordering cost = 25
H= Holding Cost = 0.50
![Q_{opt} = \sqrt{\frac{2(12,000)(25)}{0.5}}](https://tex.z-dn.net/?f=Q_%7Bopt%7D%20%3D%20%5Csqrt%7B%5Cfrac%7B2%2812%2C000%29%2825%29%7D%7B0.5%7D%7D)
EOQ = 1,095.44
Demand per day: 12,000 / 250 days = 48
Reorder point: 48 units per day x 5 days lead time = 240
Cycle time: the time it takes between orders:
365 /(12,000 / 1,095.44) = 33.3197 = 33 days
total cost:
ordering cost: 12,000 / 1,095.44 x $25 per order = $ 273.86
holding cost: 1,095.44 /2 x 0.5 = $273.86
Total: 273.86 + 273.86 = $547.52