Tree Company is a manufacturer of wooden furniture. The company produces and sells three types of wooden furniture: chairs, tables, and beds. The managers of Tree Company have collected the following information about the three products: The regular selling price is $50 per chair, $100 per table, and $150 per bed. The managers estimate that customer demands each year are 1,000 chairs, 2,000 tables, and 1,000 beds. Lumber is needed to produce the furniture. Each chair requires 10 board feet of lumber. Each table requires 20 board feet of lumber. Each bed requires 20 board feet of lumber. The company currently has only one supplier of lumber. The supplier can supply up to 50,000 board feet each year at a price of $1 per board foot. The labor hours needed to produce the furniture are 0.5 hour per chair, 0.5 hour per table, and 1.5 hours per bed. The labor capacity of the company is currently 5,000 hours each year. The hourly rate of labor is $20. The variable manufacturing overhead cost is $15 per chair, $15 per table, and $45 per bed. The variable selling cost is $5 per chair, $10 per table, and $15 per bed. The fixed manufacturing overhead cost is $200,000 each year. The fixed selling cost is $100,000 each year. Required: a. Based on the above information, determine whether a constraint exists for Tree Company. Briefly explain with supporting computations. Limit your response to 80 words. (3 marks) b. What is the optimal production plan that would maximize profit for the company? That is, how many chairs, tables, and beds should the company produce respectively? Please show ALL supporting computations. (5 marks) C. Suppose that the company finds another supplier who can provide up to 30,000 board feet of lumber each year at the same price of $1 per board foot. The new supplier does not affect the company's relationship with the existing supplier. How does this new supplier change the company's optimal production plan? That is, with the new supplier, how many chairs, tables, and beds should the company produce respectively? (1.5 marks) Suppose that the company follows the production plan that you propose in (c). A new customer approaches the company and offers to purchase 100 chairs if the company is willing to accept a 20% discount off the regular selling price. The variable selling cost would be reduced to $2 per chair. Would you recommend that the managers of the company accept this one-time offer or not? Show all supporting calculations. (3.5 marks)
