Question - Optimal Ordering Quantity for Anniversary Cards
Solution:
The image appears to contain a question related to inventory management. It refers to a situation where a manager needs to determine how many anniversary cards to order before the month of June.Given data:- Cost of each card: $1.90- Retail price for each card: $2.50- Price reduction after June: 50%- Estimated demand for cards: 4,000 units- Standard deviation of demand: 800 unitsThe manager wants to maximize the profit while minimizing the potential for unsold inventory. To address this, the manager can use the newsvendor model, which is commonly applied to problems involving perishable goods or items with a limited selling period. Essentially, the model helps in determining the optimal order quantity (Q) that maximizes the expected profit.The newsvendor model considers the following:- Co = overage cost per unit (cost when too many items are ordered)- Cu = underage cost per unit (cost when too few items are ordered)Co = cost per unit - salvage value per unitCu = price per unit - cost per unitSince the card will be reduced in price by 50%, the salvage value is half of the retail price:Salvage value = 0.5 * $2.50 = $1.25Now calculate Co and Cu:Co = $1.90 - $1.25 = $0.65Cu = $2.50 - $1.90 = $0.60Next, we calculate the critical ratio (CR), which represents the probability of selling an item (demand being greater than order quantity), and is given by:CR = Cu / (Cu + Co)CR = $0.60 / ($0.60 + $0.65)CR = $0.60 / $1.25CR = 0.48This critical ratio is then used to find the corresponding z-score from the standard normal distribution table. The z-score corresponding to a CR of 0.48 is approximately -0.05 (since a CR of 0.5 corresponds to a z-score of 0, a CR of 0.48, which is slightly lower, corresponds to a slightly negative z-score).Now that we have the z-score, we can calculate the optimal order quantity (Q*) using the following formula:Q* = (Demand mean) + z(Critical ratio) * (Standard deviation of demand)Q* = 4,000 cards + (-0.05) * 800 cardsQ* = 4,000 cards - 40 cardsQ* = 3,960 cardsTherefore, the manager should order approximately 3,960 anniversary cards.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com