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Decision Variables Closets Tables Chairs Max production 35 Min production req. Profit Q1. (30 points) Woodline Industries Inc. produces a variety of products. In a particular manufacturing process, two types of wood, mahogany and pine along with the carpenters are the main resources of the company. The company is planning to introduce a new type of closet, a new set tables and office chairs using these three main resources. Obj. function: $400 $300 $80 Constraints: LHS RHS The requirements of each product for each resources is given in the table below. 300 Mahogany Pine Carpenter Chairs req Balance req 2.5 1 5 C 1.5 2 3 4 -1 1 3 4 4 -1 C 350 600 0 0 0 Constraints: 1. Number of chairs should be more than 4 times the number of tables. 2. Number of closets and tables should be balanced. 3. A maximum of 35 should be manufactured from each product. Cm 1 If we model this problem as a linear programming problem and represent C: number of closets to be manufactured T: number of tables to be manufactured O: number of office chairs to be manufactured Answer: C (10 points) T 0 Profit And each closet set is sold for $400, each table set for $300 and each office chair for $80, Then, what number of each product should be manufactured to maximize the revenue? (Decimal numbers are OK) Carpenter hours 5 Closet set Table set Chairs set Available Mahogany (units) ) 2.5 1.5 1 300 Pine (units) 1 2 3 350 3 4 600 Decision Variables Closets Tables Chairs Max production 35 Min production req. Profit Obj. function $400 $300 $80 LHS 2.5 1 5 1.5 2 Mahogany Pine Carpenter Chairs req. Balance req. 1 3 4 -1 A A A A RHS 300 350 600 0 0 Q1.a (10 points) Suppose that Woodline Industries Inc. decided to reduce the max production requirement for each item from 35 to 30. How would this assumption change the optimal solution and the objective function? Why? 3 4 4 -1 1 1 Pine (units) Carpenter hours Answer: C (6 ponits) T 0 Profit Closet set Table set Chairs set Available Mahogany (units) 2.5 1.5 1 1 300 1 2 2 3 350 5 3 3 4 600 Answer (4 points) Why? Decision Variables Closets Tables Chairs Max production 35 $400 $300 $80 LHS Co 2.5 1 1 3 4 Q1.b. (10 points) Suppose that Woodline Industries Inc. has decided NOT to accept decimals numbers for decision variables and has asked for integer values for decision variables. Does this assumption change the optimal solution? Why? CE RHS 300 350 600 0 0 1.5 2 3 4 -1 5 CE -1 1 Pine (units) Carpenter hours Answer: C (6 ponits) T Closet set Table set Chairs set Available Mahogany (units) 2.5 1.5 1 300 1 1 2 3 350 5 3 4 4 600 Profit Answer (4 points) Why? Decision Variables Closets Tables Chairs Max production 35 Min production req. Profit Obj. function $400 $300 $80 LHS 2.5 1 CH RHS 300 350 600 Mahogany Pine Carpenter Chairs req. Balance req. . 1.5 2 3 Q1.c (10 points) Suppose that Woodline Industries Inc. decided NOT to impose the balance requirement constraint for tables and closets. How would this assumption change the optimal solution and the objective function? Why? CH 1 5 3 4 ca 4 -1 CE 0 0 1 -1 pelaunts Pine (units) Carpenter hours Answer: C (6 ponits) T o Profit Closet set Table set Mahogany (units) 2.5 1.5 1 300 1 1 2 3 350 5 5 3 4 600 Chairs set Available Answer (4 points) Why