Question

The product 'A' has the demand of 1000 with ordering cost Rs 100/- per order with a holding cost of Rs 40/- per year. Another product 'B' has the demand of 3600 with the ordering cost of Rs 100/- per year with a holding cost of Rs 100/- per year. What is the ratio of EOQs 'B' to 'A'?

• A. 1.5
• B. 1.2
• C. 2.5
• D. 3.5

Hint:

The Economic Order Quantity (EOQ) formula helps in minimizing total inventory costs (ordering and holding). Remember the formula \(EOQ = \sqrt{\frac{2DS}{H}}\) and calculate carefully. Pay attention to the ratio requested (e.g., B to A or A to B).

Answer 1

The Correct Option is B

Step 1: Recall the Economic Order Quantity (EOQ) formula.
The Economic Order Quantity (EOQ) formula is given by: \[ EOQ = \sqrt{\frac{2DS}{H}} \] Where: \(D\) = Annual Demand
\(S\) = Ordering Cost per order
\(H\) = Holding Cost per unit per year
Step 2: Calculate EOQ for Product 'A'.
For Product 'A':
Demand (\(D_A\)) = 1000 units/year
Ordering Cost (\(S_A\)) = Rs 100/- per order
Holding Cost (\(H_A\)) = Rs 40/- per year
\[ EOQ_A = \sqrt{\frac{2 \times 1000 \times 100}{40}} \] \[ EOQ_A = \sqrt{\frac{200000}{40}} \] \[ EOQ_A = \sqrt{5000} \]
Step 3: Calculate EOQ for Product 'B'.
For Product 'B':
Demand (\(D_B\)) = 3600 units/year
Ordering Cost (\(S_B\)) = Rs 100/- per order
Holding Cost (\(H_B\)) = Rs 100/- per year
\[ EOQ_B = \sqrt{\frac{2 \times 3600 \times 100}{100}} \] \[ EOQ_B = \sqrt{2 \times 3600} \] \[ EOQ_B = \sqrt{7200} \]
Step 4: Calculate the ratio of EOQs 'B' to 'A'.
Ratio = \( \frac{EOQ_B}{EOQ_A} \) \[ \text{Ratio} = \frac{\sqrt{7200}}{\sqrt{5000}} = \sqrt{\frac{7200}{5000}} = \sqrt{\frac{72}{50}} = \sqrt{\frac{36}{25}} \] \[ \text{Ratio} = \frac{\sqrt{36}}{\sqrt{25}} = \frac{6}{5} = 1.2 \]
Step 5: Compare with options.
The calculated ratio is 1.2, which matches option (2). The final answer is \( \boxed{\text{2}} \).