Answer :
The wine shop owner ordered 157 bottles.
To figure out how many bottles the wine shop owner should order, we can use the economic order quantity formula:
EOQ = √[(2DS)/(H)]
Where D = annual demand, S = cost per order, and H = holding cost per unit.
In this case, we need to adjust the formula to take into account the fact that the wine shop owner will receive a buyback price if the wine remains unsold. So the holding cost per unit is the difference between the selling price and the buyback price, or $15 - $7.5 = $7.5 per bottle.
The cost per order is the cost of the wine plus any ordering or shipping fees. In this case, the cost per order is $10 per bottle.
Plugging in the numbers, we get:
EOQ = √[(2 x 7000 x $10)/($7.5)] = 157.15
So, the wine shop owner should order approximately 157 bottles of the particular wine.
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The shop should calculate the optimal order quantity by determining the critical ratio using costs and selling prices, finding the corresponding z-score, and adjusting the order quantity based on the standard deviation of demand.
Determining the Order Quantity for a Beaujolais Nouveau Shop
The problem posed relates to a beaujolais nouveau shop's decision on how many bottles of wine to order considering the selling price, cost price, buy-back price, and demand variability. This is a typical business decision-making scenario that involves evaluating profit margins and risks associated with unsold inventory. To find the optimal order quantity, one would typically use inventory management techniques such as the Newsvendor model, which takes into account demand uncertainty and costs associated with over- and under-stocking.
In this case, the selling price is $15 per bottle, the purchase cost is $10 per bottle, and the buy-back price is $7.5 per bottle. The annual demand has a mean of 7000 bottles and a standard deviation of 1000 bottles. To maximize expected profit, the shop owner should calculate the critical ratio (which is the probability of selling a bottle during the season) and then find the corresponding z-score that matches this probability. After obtaining the z-score, use it to determine how many units above the mean they should order to optimize their inventory levels.
To calculate the critical ratio, use:
- Overage cost (Co) = Cost price - Buy back price = $10 - $7.5 = $2.5
- Underage cost (Cu) = Selling price - Cost price = $15 - $10 = $5
- Critical Ratio (CR) = Cu / (Cu + Co) = $5 / ($5 + $2.5) = 0.6667
The critical ratio can then be used to find the appropriate z-score, which in turn gives us the optimal order quantity when applied to the standard deviation of demand.
