Final answer:
To determine how many portions of scrambled eggs a hotel should order for its breakfast buffet, one can utilize a calculated approach with Poisson distribution and cost-benefit analysis, typically involving the newsvendor model to balance the cost of leftover unsold portions against the cost of losing potential sales.
Step-by-step explanation:
The question is asking how many portions of scrambled egg a hotel should order for its breakfast bar, given specific information about cost, selling price, demand distribution, and when the product becomes unsaleable. To determine the optimal number of portions to order, we can apply the concepts of Poisson distribution and cost-benefit analysis taking into account the mean demand and the costs of overshooting or undershooting this demand.Since the demand follows a Poisson distribution with a mean of 220, this means the most likely number of portions demanded is near 220. However, to precisely calculate the optimal order quantity, one would generally use the newsvendor model, which is not provided in the question's text. In such cases, if accessible, a cost-benefit analysis based on the newsvendor model will allow us to consider the cost of ordering too many portions (the leftover unsold portions at $0.55 each) versus the cost of ordering too few (lost sales opportunity at $2.20 minus $0.55 per portion). Normally, we might calculate a critical ratio which balances these costs and use that to determine the optimal point on the demand distribution to place our order figure.In absence of the exact newsvendor calculations, as a heuristic, the hotel could start by considering ordering slightly more than the mean, for example, 225 or 230 portions to account for normal variability in demand, and then adjust based on actual sales patterns observed.