Final answer:
Carlton should have the new employee work on product beta since it provides a higher contribution margin per unit of limited resource ($975) compared to product alpha ($750). This choice will result in the highest additional contribution margin and is advantageous in terms of maximizing profits.
Step-by-step explanation:
To determine which product Carlton should have the new employee work on, we need to compare the contribution margin per unit of limited resource of both products. Product alpha has a contribution margin per unit of limited resource of $750, while product beta has a $975 contribution margin per unit of limited resource. Since the employee can work 150 hours per month, we want to maximize this limited resource by choosing the product with the highest contribution margin per unit of this resource.
Comparing the two products, it is clear that product beta provides a higher contribution margin per unit of limited resource ($975) compared to product alpha ($750). Therefore, it would be more profitable for Carlton to have the new employee work on product beta, as it would result in the highest additional contribution margin. This decision aligns with the concept of marginal product and the contribution to overall profits that product beta would provide.