Example Question - anniversary cards
Here are examples of questions we've helped users solve.
Optimizing Card Orders for SEE Gift and Things
The image contains a word problem that asks how many anniversary cards the manager of SEE Gift and Things should order before the month of June. Let's solve this step by step: 1. Each card costs $1.30 and retails for $2.20. After June, the store reduces the price by 60 percent to get rid of them. First, we need to find out the reduced price of each card after the 60 percent discount. A 60 percent reduction means the customer pays 40 percent (100% - 60% = 40%) of the original retail price. Reduced price = 40% of $2.20 Reduced price = 0.40 * $2.20 Reduced price = $0.88 2. On the basis of past records, the manager has determined that the demand for these cards is 4,000 units with a standard deviation of 800. This means that the manager expects to sell 4,000 cards but there might be some variation (more or less) as indicated by the standard deviation. 3. The problem now is to calculate how many cards to order. A common approach for this kind of problem is to account for variation in demand. However, the question does not give a service level or probability, so we'll have to assume the manager wants to meet the expected demand without considering the variability (standard deviation). Thus, the manager should order the expected demand: Number of cards to order = Expected demand = 4,000 cards Therefore, the manager should order 4,000 cards.
Optimal Ordering Quantity for Anniversary Cards
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 units The 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 unit Cu = price per unit - cost per unit Since the card will be reduced in price by 50%, the salvage value is half of the retail price: Salvage value = 0.5 * $2.50 = $1.25 Now calculate Co and Cu: Co = $1.90 - $1.25 = $0.65 Cu = $2.50 - $1.90 = $0.60 Next, 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 / $1.25 CR = 0.48 This 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 cards Q* = 4,000 cards - 40 cards Q* = 3,960 cards Therefore, 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