ABC Inc. stocks standard length, 25-foot rugs, which it cuts to custom lengths to fill individual customer orders. An order has just come in for 5,000 7-foot rugs, 1,200 9-foot rugs, and 300 11-foot rugs. The company manager has identified six ways to cut the 25-foot rugs to fill this order. The six cutting patterns are summarized in the following table. Number of Rugs Produced Cutting Pattern 7 ft 9 ft 11 ft 11 0 0 o o 2 1 3 OnNw 0 1 14 2 lo 5 1 1 16 0 0 2 One possibility (cutting pattern 1) is to cut a 25-foot rug into three 7-foot rugs, and not to cut any 9- or 11-foot rugs. Note that cutting pattern 1 uses a total of 21 feet of rug and leaves a 4-foot piece of scrap. Another possibility (cutting pattern 4) is to cut a 25-foot rug into one 7-foot rug and two 9-foot rugs (using all 25 feet of the rug). The remaining cutting patterns have similar interpretations. The company manager wants to fill this order using the fewest number of 25-foot rugs as possible. To do this, the manager needs to determine how many 25-foot rugs to run through each cutting pattern. The LP for this problem is: Xi = number of rugs to which cutting pattern i is applied Xi = number of rugs to which cutting pattern i is applied MIN X1 + X2 + X3 + X4 + X5 + X6 ST 3X1 + 2x2 + 2x3 + 1X4 + OX5 + OX6 >= 5,000 OX1 + 1X2 + OX3 + 2x4 + 1X5 + OX6 >= 1,200 OX1 + OX2 + 1X3 + OX4 + 1X5 + 2X6 >= 300 Xi >= 0 & integer Implement this LP. Using the output from your spreadsheet, update the following chart. Remember to upload your spreadsheet to ACORN. Cutting Number of Number of rugs cut Pattern times used 7 ft 9 ft 11 ft 1 3 o 0 2 - 2 11 0 3 2 0 1 14 2 0 5 O 1 1 0 0 2 Rugs produced Rugs 5,000.0 1,200.0 300.0 required Total # of 25' rugs 2,167.00 cut ABC Inc. stocks standard length, 25-foot rugs, which it cuts to custom lengths to fill individual customer orders. An order has just come in for 5,000 7-foot rugs, 1,200 9-foot rugs, and 300 11-foot rugs. The company manager has identified six ways to cut the 25-foot rugs to fill this order. The six cutting patterns are summarized in the following table. Number of Rugs Produced Cutting Pattern 7 ft 9 ft 11 ft 11 0 0 o o 2 1 3 OnNw 0 1 14 2 lo 5 1 1 16 0 0 2 One possibility (cutting pattern 1) is to cut a 25-foot rug into three 7-foot rugs, and not to cut any 9- or 11-foot rugs. Note that cutting pattern 1 uses a total of 21 feet of rug and leaves a 4-foot piece of scrap. Another possibility (cutting pattern 4) is to cut a 25-foot rug into one 7-foot rug and two 9-foot rugs (using all 25 feet of the rug). The remaining cutting patterns have similar interpretations. The company manager wants to fill this order using the fewest number of 25-foot rugs as possible. To do this, the manager needs to determine how many 25-foot rugs to run through each cutting pattern. The LP for this problem is: Xi = number of rugs to which cutting pattern i is applied Xi = number of rugs to which cutting pattern i is applied MIN X1 + X2 + X3 + X4 + X5 + X6 ST 3X1 + 2x2 + 2x3 + 1X4 + OX5 + OX6 >= 5,000 OX1 + 1X2 + OX3 + 2x4 + 1X5 + OX6 >= 1,200 OX1 + OX2 + 1X3 + OX4 + 1X5 + 2X6 >= 300 Xi >= 0 & integer Implement this LP. Using the output from your spreadsheet, update the following chart. Remember to upload your spreadsheet to ACORN. Cutting Number of Number of rugs cut Pattern times used 7 ft 9 ft 11 ft 1 3 o 0 2 - 2 11 0 3 2 0 1 14 2 0 5 O 1 1 0 0 2 Rugs produced Rugs 5,000.0 1,200.0 300.0 required Total # of 25' rugs 2,167.00 cut