Company ABC is a manufacturing company specialized in three auto parts denoted by X, Y, and Z respectively. The company is preparing for the budgets for the next year and has collected the following information:

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a.The company allocates $10 of variable overhead cost to each labor hour.

b.The total fixed cost for the entire company is $300,000.

c.The company has a total labor budget of $50,000 with an hourly labor cost of $10.

d.After calculation, it costs $0.5 to run the machine for 1 hour. Company's total budget for running machine is $20,000.

1. Does the company have any constraint? If yes, what is the constraint? (2 marks)

2. Given the constraint, what is the optimal production plan for the company that maximizes the company's profit? (4 marks)

3. Company ABC has another two products: A and B. A can be sold "as is" (price: $300) or processed further into product A1 (price: $500). B can be sold "as is" (price: $200) or processed further into product B1 (price: $280). The allocated joint costs of A and B are $20 and $10, respectively. The cost of further processing costs of A and B are $180 and $77, respectively. Which product should be processed further and why? (4 marks)