Final answer:
The average profit function P(x) involves integrating the given profit function, but average profit at x=0 is undefined. For non-zero values of x, it can be calculated by dividing total profit by the quantity of grills sold, as illustrated in the provided example where a profit is made on the sale of 40 thousand grills.
Step-by-step explanation:
The average profit function P(x) can be found by integrating the profit function P(x) = 40x - 0.8x² - 255 and then dividing by the quantity x. However, the student is likely asking to find the average profit itself, rather than its function, and for a specific value of x, where x = 0. We can't compute the average profit for x = 0 because the average profit is undefined when no grills are sold (as we would be dividing by zero). If we consider finding the profit for a given number of grills sold that is not zero, for instance, x = 40 as given in the accompanying example where the firm sells 40 thousand grills for a price of $16 per grill, resulting in a total revenue of $640 thousand and total costs of $580 thousand which yields a profit of $60 thousand, we can then calculate the average profit per thousand grills by dividing $60 by 40, obtaining an average profit of $1.5 thousand per thousand grills.