Question

A daily newspaper is stocked by a coffee shop so its patrons can purchase and read it while they drink coffee. The newspaper costs $1.16 per unit and sells for $1.75 per unit. If units are unsold at the end of the day, the supplier takes them back at a rebate of $1 pet unit. Assume that daily demand is approximately normally distributed with μ=150 and σ=30. (a) What is your recommended daily order quantity for the coffee shop?

Answer 1

The recommended daily order quantity for the coffee shop can be determined using the newsvendor model by balancing the costs and revenues, and factoring in the normal distribution of the newspaper demand with a mean of 150 and a standard deviation of 30.

Step-by-step explanation:

To recommend a daily order quantity for the coffee shop, we need to maximize the expected profit which involves balancing the cost of ordering newspapers with the potential revenue from them and potential loss from unsold papers. The cost to purchase one newspaper is $1.16, which can be sold for $1.75, resulting in a profit per sold unit of $0.59. For unsold papers, the supplier provides a rebate of $1, representing a loss per unsold unit of $0.16 ($1.16 - $1).

Given that the daily demand for newspapers is normally distributed with a mean (μ) of 150 and a standard deviation (σ) of 30, we can use the newsvendor model. The critical ratio (CR) for this problem is the probability of selling a newspaper without going over the demand, which is calculated as the profit from selling a unit divided by the sum of the profit and the loss from an excess unit (0.59/(0.59+0.16)). We then find the z-score that corresponds to this CR in the standard normal distribution and calculate the optimal order quantity by using the formula Q* = μ + z* σ.