Final answer:
To decide how many cases of tomatoes to stock, construct a pay-off matrix and use the Maximum Likelihood approach, stocking the number of cases with the highest sales probability from the historical data, considering potential losses from unsold inventory.
Step-by-step explanation:
When determining how many cases of tomatoes to stock in a market where the sales quantity is uncertain, constructing a pay-off matrix is crucial for visualizing the potential outcomes of different decisions. The cost to purchase a case of tomatoes is =N=3,000 and the selling price is =N=8,000, leading to a profit of =N=5,000 per case sold. The pay-off matrix would include potential profits and losses based on the probability of selling a given number of cases.
Using the Maximum Likelihood approach, which recommends selecting the decision with the highest chance of occurring (based on historical data), we look for the number of cases with the highest probability, which here seems to be 0.4. Without more detailed information about the distribution of sales probabilities and corresponding sales quantities, a complete answer is not feasible. However, based on this approach, we would choose to stock the number of cases that corresponds with the highest probability of sales from past data while considering the perishable nature of the good and potential losses from unsold inventory.
In the provided scenario about the farm and raspberries, it was determined that operating at a price that covered variable costs even at a loss was preferable to shutting down entirely due to the profit-maximizing output level rule where price exceeded average variable cost. When prices fell below average variable cost, shutting down and only incurring fixed costs was considered the better course of action. Despite being a different context and product, the concept of analyzing costs against probable revenue to determine the best course of action applies to the tomato sales problem.