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$3$ Sales Mix with Limited Resources

Sam can only hire two full$-$time employees, but he needs even more help to make the two products he sells. Product Alpha has a contribution margin of $$750$ per unit of limited resource and Product Beta has a contribution margin of $$975$ per unit of limited resource. He thinks he will be able to afford hiring an extra employee to work $150$ hours per month, but he is unsure which product to have the employee work on$.$ Which product would result in the highest contribution margin?

Product Alpha, which would provide additional contribution margin of $$500,000$

Product Alpha, which would provide additional contribution margin of $$112,500$

Product Beta, which would provide additional contribution margin of $$650,000$

Product Beta, which would provide additional contribution margin of $$146,250$