Final answer:
The assertion is false, as both variable and fixed costs are relevant when deciding whether to eliminate a product. While variable costs fluctuate with production, fixed costs must still be accounted for as part of total costs that need to be exceeded by total revenue for profitability.
Step-by-step explanation:
The statement 'Only the variable costs identified with a product are relevant in a decision concerning whether to eliminate the product or not' is false. While variable costs are indeed relevant because they can change with production levels, it is important to consider total costs, which include both variable and fixed costs. Although fixed costs are often sunk and cannot be recovered, they still play a role in the short-run financial outlook of a product since they are part of the total costs that must be covered by total revenue for the firm to earn a profit.
In the context of deciding whether to continue or eliminate a product, fixed costs should not be ignored entirely, because they contribute to the total cost that must be exceeded by total revenue. Variable costs provide critical information on the firm's ability to cut costs and the extent to which costs will increase if production rises, indicating how future changes in production levels might impact profitability.