Farrell Manufacturing Company produces several products that are used by hospitals. Information concerning these products is attached.

Since the products are manufactured using a highly technical process, workers cannot be easily trained and production is constrained by the number of labor hours available. The company has $50,000$ direct labor hours available per year and each worker is paid an average of $$20$ per hour.

REQUIRED: $(1)$ Using the attached form, calculate the contribution margin per unit for each product.

$(2)$ Using the attached form, calculate the contribution margin per unit of scarce resource.

$(3)$ Using the attached form, show how you would allocate the company's production capacity among the various products in order to maximize the company's profits. Provide appropriate supporting computations to justify your answer.