This problem involves determining the optimal order quantity for the store based on the newsvendor model, where we balance the cost of overstocking (excess onions) and understocking (lost goodwill).

The steps are as follows:

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Given Data:

• Selling Price (S): Rs. 50 per kg
• Wholesale Price (C): Rs. 30 per kg
• Salvage Price (V): Rs. 15 per kg
• Goodwill Loss (G): Rs. 10 per kg
• Expected Demand Distribution: $N(100, 16^2)$

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Step 1: Calculate Marginal Costs

1. Cost of Understocking (CU):
   This is the loss when a unit is out of stock, including goodwill loss and lost profit:
   $CU = S - C + G = 50 - 30 + 10 = 30 \, \text{Rs per kg.}$

2. Cost of Overstocking (CO):
   This is the loss when a unit remains unsold, accounting for salvage value:
   $CO = C - V = 30 - 15 = 15 \, \text{Rs per kg.}$

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Step 2: Critical Ratio ($CR$)

The critical ratio determines the probability of meeting the demand:
$CR = \frac{CU}{CU + CO} = \frac{30}{30 + 15} = 0.6667$

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Step 3: Optimal Stocking Level

Using the critical ratio, we find the z-value corresponding to the cumulative probability $CR = 0.6667$ from the standard normal distribution table:
$z = 0.43 \quad (\text{approximately from z-tables or statistical tools})$

The optimal stocking level $Q$ is then determined using the mean $\mu = 100$ kg and standard deviation $\sigma = 16$ kg:
$Q = \mu + z \cdot \sigma = 100 + 0.43 \cdot 16 = 100 + 6.88 = 106.88 \, \text{kg.}$

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Final Answer:

The store should stock 107 kg of onions (rounded to the nearest kilogram) to balance the costs effectively.

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Would you like a detailed breakdown of any part or further clarifications? 😊

Here are 5 related questions to explore:

1. What happens to the stocking level if the standard deviation of demand increases?
2. How does a lower goodwill loss affect the optimal stocking quantity?
3. How would the optimal stocking level change if the salvage price increases?
4. Can this analysis be extended to multiple products with different demand patterns?
5. How would the result change if demand follows a distribution other than normal?

Tip: Keep a table of z-scores handy for quick access during such problems!