STAR Co provides paper to smaller companies with volumes that are not large enough to warrant dealing directly with the paper il STAR receives 100-feet-wide paper rolls from the mil and cuts the rolls into smaller rolls of widths 12, 15, and 30 feet. The demands for these widths vary from weak to week. The following cutting patterns have been established Pattern Number 12-1t 15 ft 30-ft Trim Loss (ft) 0 6 0 10 2 0 0 3 10 3 B 0 4 4 3 0 2 4 5 7 1 0 1 Trimboss is the leftover paper from a pattern for pattum 4,3(12)+(15) 2(30) 96 tented results in 100 - 964 foot of trim fon). Orders in hand for the coming we are 5,680 12-foot rolls, 1,670 15-foot rolls, and 3,340 30-foot rolls. Any of the three types of reproduced in excess of the orders in hand will be sold on the open market at the selling price No inventoryheid (a) Formulate an integer programming model that will determine how many 100-foot rolls to cut into each of the five patterns horder to minime trimit (Let - number of rolls out into pattern, for- 1,2,3,4,5) Min 12. 15.1 P, = number of rolls cut into pattern I, for} = 1, 2, 3, 4, 5.) Min s.t. 12-ft 15-ft 30-ft PP2, P3, Pa, Pg 20 (b) Solve the model formulated in part (a). What is the minimal amount of trim loss (in ft)? 2007 X ft How many of each pattern should be used? Pattern 1 0 rolls Pattern 2 0 rolls 0 rolls Pattern 3 Pattern 4 1675 332 Xrolls X rolls Pattern 5 How many of each type of roll will be sold on the open market? 12.ft 5670 15-ft 1683 30-ft 3366 Xrolls Xrolls Xrolls STAR Co provides paper to smaller companies with volumes that are not large enough to warrant dealing directly with the paper il STAR receives 100-feet-wide paper rolls from the mil and cuts the rolls into smaller rolls of widths 12, 15, and 30 feet. The demands for these widths vary from weak to week. The following cutting patterns have been established Pattern Number 12-1t 15 ft 30-ft Trim Loss (ft) 0 6 0 10 2 0 0 3 10 3 B 0 4 4 3 0 2 4 5 7 1 0 1 Trimboss is the leftover paper from a pattern for pattum 4,3(12)+(15) 2(30) 96 tented results in 100 - 964 foot of trim fon). Orders in hand for the coming we are 5,680 12-foot rolls, 1,670 15-foot rolls, and 3,340 30-foot rolls. Any of the three types of reproduced in excess of the orders in hand will be sold on the open market at the selling price No inventoryheid (a) Formulate an integer programming model that will determine how many 100-foot rolls to cut into each of the five patterns horder to minime trimit (Let - number of rolls out into pattern, for- 1,2,3,4,5) Min 12. 15.1 P, = number of rolls cut into pattern I, for} = 1, 2, 3, 4, 5.) Min s.t. 12-ft 15-ft 30-ft PP2, P3, Pa, Pg 20 (b) Solve the model formulated in part (a). What is the minimal amount of trim loss (in ft)? 2007 X ft How many of each pattern should be used? Pattern 1 0 rolls Pattern 2 0 rolls 0 rolls Pattern 3 Pattern 4 1675 332 Xrolls X rolls Pattern 5 How many of each type of roll will be sold on the open market? 12.ft 5670 15-ft 1683 30-ft 3366 Xrolls Xrolls Xrolls
