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Use the following scenario and data for questions 31 to 40: Joe's Furniture, LLC, manufactures both press wood bookshelves and desks. Management wants to develop a linear programming model to determine the numbers of bookshelves and desks to better utilize the labor resources. The contributions to fixed cost and profit each bookshelf and each desk are $11 and $13, respectively. The following table gives labor requirements in the Cutting, Drilling and Packaging departments, as well as the total number of labor hours available in each department per day 2.2 Drilling Product Department Total Bookshelf Desk Cutting 2.5 1200 1.8 1.4 1000 Packaging 0.9 1.2 560 Suppose some workers in the three departments are cross-trained and can be transferred from one department to another. The permitted transfers and the maximum labor hours transferable from each department are listed in the following table. From To Department Maximum labor Department Cutting Drilling Packaging Hours Transferable Cutting Yes Yes 200 Drilling Yes Yes 150 Packaging Yes 100 - You are required to formulate a linear programming model to maximize the total contribution to fixed cost and profit. QUESTION 31 Reasonable definitions of the decision variables are O X1 --number of bookshelves to make per day X2 -- number of desks to make per day t12 - number of labor hours transferred from Cutting to Drilling t13 - number of labor hours transferred from Cutting to Packaging t21 -- number of labor hours transferred from Drilling to Cutting t23 -- number of labor hours transferred from Drilling to Packaging t32 -- number of labor hours transferred from Packaging to Drilling O X1 -- cost of bookshelves to make X2 -- cost of desks to make t 12 -- number of labor hours transferred from Cutting to Drilling t13 - number of labor hours transferred from Cutting to Packaging 121 -- number of labor hours transferred from Drilling to Cutting 23 -- number of labor hours transferred from Drilling to Packaging 132 -- number of labor hours transferred from Packaging to Drilling O X1 - number of bookshelves to make per day X2 -- number of desks to make per day t 12 -- number of labor transferred from Cutting to Drilling t 13 -- number of labor transferred from Cutting to Packaging t21 -- number of labor transferred from Drilling to Cutting t23 -- number of labor transferred from Drilling to Packaging t32 -- number of labor transferred from Packaging to Drilling O All of the above are reasonable definitions. O None of the above. QUESTION 32 The correct objective function is O min 11x1 + 13x2 O max 11x1 + 13x2 max 11x1 + 13x2 +t12+t13+t22 + t23 +t32 O min 11x1 + 13x2 +t12 + t 13 +t22 + t23 +t32 O none of the above QUESTION 33 The correct constraint restricting the use of labor hours in cutting not to be more than the availability considering the labor transfers among different departments is O 2.5X1 +2.2x2 5 1200 O 2.5x1+2.2x2 - 612 - +13 +421 51200 O 2.5X1+2.2x2 + +12+13 - 12151200 2.5x2 +2.2X2 + + 12 +113 1200 none of the above QUESTION 34 The correct constraint restricting the use of labor hours in drilling not to be more than the availability considering the labor transfers among different departments is O 1.8X1+1.4x2