Final answer:
Product A should be processed further before selling because the additional revenue of $18,000 from further processing is greater than the additional cost of $15,000, increasing profits by $3,000.
Step-by-step explanation:
The question pertains to the decision about whether to sell product A at the split-off point or to process it further. To determine the correct course of action regarding product A, we need to assess the additional revenue generated versus the additional processing costs. At the split-off point, product A can be sold for $40,000. If processed further, it incurs an additional cost of $15,000 but then can be sold for $58,000. The incremental revenue from processing further is $58,000 - $40,000 = $18,000, which is greater than the additional processing cost of $15,000. Therefore, the company will increase profits by $3,000 ($18,000 - $15,000) by processing product A further before selling it.