Let's solve the problem step-by-step to determine which item should be stored at the very back of the warehouse.
### Step 1: Understanding the Problem
We are given the weekly demand and space required for five different items (A, B, C, D, and E). To determine which item should be stored furthest away from the dock, we need to find the item with the smallest importance based on demand relative to space.
### Step 2: Calculate the Ratio
The ratio of weekly demand to space required will tell us how important an item is in terms of storage efficiency. We calculate this ratio for each item as follows:
[tex]\[
\text{Ratio} = \frac{\text{Weekly Demand}}{\text{Space Required}}
\][/tex]
### Step 3: Calculate Ratios for Each Item
Let's calculate the ratio for each item using the given data:
- Item A:
[tex]\[
\text{Ratio}_A = \frac{300}{60} = 5.0
\][/tex]
- Item B:
[tex]\[
\text{Ratio}_B = \frac{220}{3} \approx 73.33
\][/tex]
- Item C:
[tex]\[
\text{Ratio}_C = \frac{72}{1} = 72.0
\][/tex]
- Item D:
[tex]\[
\text{Ratio}_D = \frac{60}{10} = 6.0
\][/tex]
- Item E:
[tex]\[
\text{Ratio}_E = \frac{24}{3} = 8.0
\][/tex]
### Step 4: Compare Ratios
After calculating, we have the following ratios:
[tex]\[
\text{Ratios} = \{ \text{A}: 5.0, \text{B}: 73.33, \text{C}: 72.0, \text{D}: 6.0, \text{E}: 8.0 \}
\][/tex]
### Step 5: Find the Smallest Ratio
We compare the ratios to find the smallest one:
[tex]\[
\min(5.0, 73.33, 72.0, 6.0, 8.0) = 5.0
\][/tex]
The smallest ratio is 5.0, which corresponds to item A.
### Conclusion
Therefore, the item that should be stored at the very back of the warehouse, furthest away from the dock, is:
[tex]\[
\boxed{\text{Item A}}
\][/tex]
