Example Question - profit maximization
Here are examples of questions we've helped users solve.
Profit Maximization Decision Rules Correction
For question 19, regarding profit maximizing decision rules, the statement that is incorrect is: C. MC should always be greater than MR to maximize profit. This statement is incorrect because to maximize profit, a firm should produce up to the point where marginal cost (MC) is equal to marginal revenue (MR), not where MC is greater than MR. Producing where MC is greater than MR would mean the firm is producing too much and would decrease its profitability. The correct profit-maximizing condition is when MC = MR, as stated in option D. Therefore, option C is the incorrect statement.
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