Final answer:
The model provided to Dave predicts the sales of spices based on their price; however, its reliability is questionable without validation data. For example, at the lower price limit, it predicts zero sales, and at the higher price limit, it predicts negative sales, both of which appear unrealistic.
Step-by-step explanation:
The question relates to the construction of a linear model and its application to predict sales based on the cost of a product. In this instance, Dave has a spice store and has a model provided by a consultant that predicts sales (in pounds per week, s) to be 20 - 4P, where P is the price per pound of the spice in dollars.
To determine if Dave should rely on this model, we would need to assess its accuracy based on historical sales data, its assumptions, and how well it reflects real-world conditions. However, without more information on its development and validation, it's challenging to make an informed decision on its reliability.
As an example, if Dave prices a spice at $5 per pound, according to the model, the sales prediction would be s = 20 - 4(5) = 20 - 20 = 0.
This raises a question, because it would mean no sales at $5 per pound, which may not be a realistic prediction. Similarly, at $10 per pound, the model predicts s = 20 - 4(10) = 20 - 40 = -20 pounds of sales, which is impossible in practical terms.
Overall, Dave should critically assess the model's assumptions, validate it against actual sales data, and consider factors beyond price that may influence sales, such as marketing, customer preferences, and competition.