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Use the following scenario and data for questions 41 to 50: Superior Sewing, Inc. makes dress pants, casual pants, and shorts of different sizes. The received orders for the next month are 3000 pairs of dress pants, 4500 pairs of casual pants and 1500 pairs of shorts. However, these orders are out of Superior Sewing's production capacity. Hence, it needs to subcontract some of the production to other clothes manufacturers. Its capacity is limited to 6500 hours of sewing time. In addition, the availability of fabrics may also limit its production. It has 6800 yards of fabrics available for the next month. The following table gives the usages of sewing time and fabrics by each product and also gives the manufacturing and purchase cost of each product. Because of cost difference, Superior Sewing needs to decide the units of each product to make in house and to purchase from other manufacturers. While satisfying demands, Superior Sewing would like to minimize its total cost. A linear programming model is appropriate for this problem. Purchase 15 1.10 1.25 1.00 18 15 9 8 Product Resource Requirement Cost ($) Sewing Time (hours) Fabrics (yards) Manufacture Dressing Pants 1.25 1.20 Casual Pants 13 Shorts 0.85 Availability 6500 6800 The following are the decision variables used in the model: An-number of pairs of dress pants to manufacture 12- number of pairs of dfess pants to purchase xy-number of pairs of casual pants to manufacture *32 - number of pairs of casual pants to purchase 131 - number of pairs of shorts to manufacture X32 - number of pairs of shorts to purchase The following is the linear programming model: min 15x1 +18x12 +13x21 +15X22 +8x31 +9x32 S1 2 3000 12 x2+x22 4500 1500 1.25 *11 x3 + x2 > +0.85 S X31 +1.10 X21 6500 The following is the linear programming model: min 15x21 +18x12 +13x21 +15x22 +8xz1 +9x32 + S.T. 2 3000 12 x21 + x22 VV IV 4500 1500 1.25 +1.10 X21 x3 + x32 2 +0.85 s X31 5 6500 *11 +1.00 X31 > > B D E F G H 1 K WN- Total Cost 15 18 13 15 8 60 9 121000 Constraints 1 1 1 1 1 3000 2 4500 2 1500 2 6500 S 6725 S 3000 4500 1500 6500 6800 1 0.85 1 1.25 1.2 1.1 1.25 7 8 9 10 11 12 Variables X11 X12 X21 X22 X31 3000 0 2500 2000 Sheet1 Sheet2 Sheet3 X32 0 1500 H4 Sensovity Report 1 Ready 100% x D 2 P5.xlsx - Microsoft Excel 2 px File Hon Inse Pag For Dati Revi Vier Load JMP Acre Teat J36 fx OK. > A B D E F G 13 14 Objective Cell (Min) 15 Cell Name Original Value Final Value 16 $J$3 Total Cost 121000 121000 17 18 19 Variable Cells 20 Cell Name Original Value Final Value Integer 21 $D$1 X11 3000 3000 Contin 22 $E$1 X12 0 O Contin 23 $F$1.X21 2500 2500 Contin 24 $G$1 X22 2000 2000 Contin 25 SH$1 X31 0 O Contin 26 $I$12X32 1500 1500 Contin 27 28 29 Constraints 30 Cell Name Cell Value Formula Status Slack 31 $J$S Constraints 3000 $J$5>$L$5 Binding 0 32 SJ$6 4500 $J$6>=$L$6 Binding 0 33 $J$ 7 1500 $J$7>$L$7 Binding 0 34 SJ$8 6500 $J$8 X 0 File P5.xlsx - Microsoft Excel Home Insert Page Formul Data Review View Load TUMP Acrobe Team A1 f Microsoft Excel 14.0 Sensitivity Report 0 > 3 I H A B D E 1 Microsoft Excel 14.0 Sensitivity Report 2 Worksheet: (P3.xlsx]Sheet1 3 Report Created: 12/20/2018 4:38:27 PM 4 5 6 Variable Cells 7 Final Reduced Objective Allowable Allowable 8 Cell Name Value Cost Coefficient Increase Decrease 9 $D$12 X11 3000 0 15 0.727272727 17.27272727 10 $E$12 X12 0 0.727272727 18 1E430 0.727272727 11 $F$12 X21 2500 0 13 0.705882353 0.64 12 $G$12 X22 2000 0 15 0.64 0.705882353 13 SH$12 X31 0 0.545454545 8 1E+30 0.545454545 14 SI$12 X32 1500 0 9 0.545454545 9 15 16 Constraints 17 Final Shadow Constraint Allowable Allowable 18 Cell Name Value Price R.H. Side Increase Decrease 19 $J$5 Constraints 3000 17.27272727 3000 2200 340.2061856 20 $J$6 4500 15 4500 1E+30 2000 21 SI$7 1500 9 1500 1E+30 1500 22 $J$8 6500 -1.818181818 6500 66 2750 23 SJ$9 6725 0 6800 1E+30 75 -24 Sensitivity Report 1 Sheet1 Sheet2 SO Ready HA 100% QUESTION 41 The number of pairs of dress pants to be manufactured is O 3000 O 2500 O 2000 none of the above QUESTION 42 The number of pairs of dress pants to be purchased is O 3000 O 2500 O 2000 O none of the above QUESTION 43 The total manufacturing cost of the three products is O $45000 $32500 O $77500 O $121000 O none of the above QUESTION 44 The total purchase cost of the three products is O $0 O $30000 O $13500 $43500 O none of the above QUESTION 45 The sewing time in hours used for casual pants is O 2750 4950 O 3750 O none of the above QUESTION 46 The surplus capacity in hours, i.e., time left over, in sewing time is O 2750 0 4950 O 3750 O none of the above QUESTION 47 The total amount of fabrics used for casual pants is O 3125 O 2500 O 5625 O 6800 O none of the above QUESTION 48 The total manufacture and purchase cost of casual pants is $2500 O $2000 $32500 $30000 O none of the above QUESTION 49 What strictly restricts the quantities of the three products manufactured for this optimal solution? O sewing time only O fabrics only O neither sewing time nor fabrics both sewing time and fabrics O not enough information to determine QUESTION 50 Which of the following does the dual price of -1.8182 for constraint 4 mean if one additional hour of sewing time becomes available? The total manufacture and purchase cost will increase by $1.8182 The total manufacture and purchase cost will decrease by $1.8182. The number of pairs of dress pants manufactured will increase by 1.818.2 The number of pairs of casual pants manufactured will increase by 1.8182. The number of pairs of shorts manufactured will increase by 1.8182