Certainly! Let's go through the steps to find the required information based on the given data:
Given:
- Yearly demand (D) = 40,000 units
- Re-ordering quantity (Q) = 4,000 units
- Procurement cost per procurement (S) = Rs. 100
### Step-by-Step Solution:
### a. Holding Cost per Unit per Year:
1. Determine the number of orders per year:
To find the number of orders per year, we divide the yearly demand by the re-ordering quantity:
[tex]\[
\text{Number of orders} = \frac{\text{Yearly demand}}{\text{Re-ordering quantity}} = \frac{40000}{4000} = 10
\][/tex]
2. Calculate the average inventory:
The average inventory level is obtained by taking half of the re-ordering quantity:
[tex]\[
\text{Average inventory} = \frac{\text{Re-ordering quantity}}{2} = \frac{4000}{2} = 2000 \text{ units}
\][/tex]
3. Calculate the holding cost per unit per year:
We need to get the holding cost per unit per year. The holding cost (H) is obtained using the formula:
[tex]\[
H = \frac{\text{Procurement cost per procurement}}{\text{Average inventory}}
\][/tex]
Substituting the values, we get:
[tex]\[
H = \frac{100}{2000} = 0.05 \text{ Rs. per unit per year}
\][/tex]
### b. Total Carrying Cost:
4. Calculate the total carrying cost:
Carrying cost is the cost of holding inventory and is given by the product of the holding cost per unit per year and the average inventory:
[tex]\[
\text{Total carrying cost} = \text{Holding cost per unit per year} \times \text{Average inventory}
\][/tex]
Substituting the values:
[tex]\[
\text{Total carrying cost} = 0.05 \times 2000 = 100 \text{ Rs. per year}
\][/tex]
### Summary:
- Holding cost per unit per year: Rs. 0.05
- Total carrying cost: Rs. 100
These detailed steps explain the intermediate calculations used to find the holding cost per unit per year and the total carrying cost.
