Calculation of Economic Order Quantity (EOQ):

EOQ formula = √[(2 x annual requirement x ordering cost) / carrying cost per unit per month]

Substituting the given values, we get:

EOQ = √[(2 x 50000 x Cp) / (1.25% x 1.20)]
EOQ = √[(100000 x Cp) / 0.015]
EOQ = √[6666666.67 x Cp]

Calculation of Total Cost:

Total cost = (EOQ/2) x Cp + (annual requirement/EOQ) x ordering cost + (EOQ x carrying cost per unit per month/2)

Substituting the given values, we get:

Total cost = (5000/2) x Cp + (50000/5000) x Cp + (5000 x 0.0125/2)
Total cost = 2500Cp + 50Cp + 31.25
Total cost = 2550.5Cp

Explanation:

- Economic Order Quantity (EOQ) is the optimal order quantity that minimizes the total cost of inventory management.
- In this case, the given values are annual requirement, ordering cost, carrying cost per unit per month, and price.
- Using the EOQ formula, we can calculate the EOQ as √[6666666.67 x Cp].
- The total cost of inventory management is the sum of ordering cost, carrying cost, and purchase cost.
- Purchase cost is calculated as the product of price and annual requirement.
- By substituting the given values in the total cost formula, we get the total cost as 2550.5Cp.
- Therefore, the company should order 5000 units at a time and the total cost of inventory management would be 2550.5 times the ordering cost.