Modular Design for the Help-You Company The Help You Company is in the business of manu- facturing first-aid kits for cars, hikers, campers, sports teams, and scouting groups. The company is located in Tucson, Arizona, and all materials must be sent to Tucson and then shipped to customers' warehouses. The company has done extensive market surveys of its customers; Table 26 shows its estimates for the de- mand for its kits in the coming year. Each kit contains the individual items shown in Table 27, which are listed with their base sizes in pounds. Help- You, for example, can buy packs of Acetaminophen extra-strength caplets. Each pack con- tains 12 tablets and costs Help You $1.50. Help-you buys the individual items and then as- sembles kits based on the requirements for each part in each kit as shown in Table 28. These are minimum requirements in that the cus- tomer expects at least the listed quantity of each item in each specific kit. For example, in the kit for campers, there must be at least four blankets and at least three cold units (six cold packs) as well as the other items. There are two strategies available for assembly of the kits: In direct assembly, the exact requirements are put into each kit. In modular assembly, one or more standard mod- ules are developed that can be assembled and com- bined into a kit with enough modules so that the minimum requirements for each item are met. A graphic of the approach is detailed in Figure 5. If you design a module, for example, that has two units of Band-Aids (as well as the other items) and place three of these modules in a scouting kit, then the kit will have 3*2 = 6 units of Band-Aids; this will meet the requirement of four units of Band-Aids for scouting kits. In this example, there is an "overage" of two extra units of Band-Aids that costs 2* $i per unit = $2 per cach scout kit demanded. Also, the total unit con- tent in a module cannot weigh more than 15 pounds (an assembly requirement). Direct assembly meets requirements exactly, al- though it usually has higher labor costs than modular assembly. For storing inventory, modules are easier to use because they tend to be smaller than kits. Develop a strategy for modular assembly. The key costs of the modular system are the overages that oc- cur. Your strategy must include the following: the number of modules you are designing the more modules you have, the closer you can match re- quirements exactly, although the higher the costs for assembly and inventory); the unit content of each module designed; and an estimate for the total number of each module required. Your analysis should consider issues such as: the trade-off between the number of different mod- ules designed and the total overage cost (you do not need to try more than five different modules why?); TABLE 26 Kit Demand Type Number of Kits Sold Cars Hikers Campers Sports teams Scouting groups 1,000 800 100 200 300 Cost (5) Base Unit Weight (Lb.) 0.20 0.20 4 TABLE 27 Item Cost and Base Size Item Adhesive Band-Aids Ace bandages Flares Blankets Adhesive tape Cold packs Sunburn cream Antiseptic cream Acetaminophen extra-strength caplets Rubber gloves Base Unit 10 per pack 1 bandage 3 per pack 1 blanket I roll 2 per pack 1 tube I tube 12 tablets 2.50 4 1.00 2.00 0.40 0.80 0.40 0.50 0.30 3.50 1.50 1.50 3 pairs 0.20 TABLE 28 Item to Kit Requirements (Base Units) Kit Hem Sports Teams Scouting Groups Cars 1 Hikers 2 Campors 4 1-ON Ace bandages Band-Aids Flares Blankets Adhesive tape Cold packs Sunburn cream Antiseptic cream Acetaminophen caplets Rubber gloves 2 2 2 2 - -MMM - - - FIGURE 5 Modular Assembly Hiker Camping Sports Scouts Modules Band-Aids Gloves Ace bandage Tape Flares Blankels the sensitivity of your solution to the kit demand estimates (for example, what happens to your rec- ommendations if the number of scouting kits sold changes by 20%?); the sensitivity of your recommendations to the unit cost values; the sensitivity of your recommendations to the weight limit on the size of each module; and discussion about your confidence that you have the optimal solution in light of what you have covered concerning convex functions and sets. Modular Design for the Help-You Company The Help You Company is in the business of manu- facturing first-aid kits for cars, hikers, campers, sports teams, and scouting groups. The company is located in Tucson, Arizona, and all materials must be sent to Tucson and then shipped to customers' warehouses. The company has done extensive market surveys of its customers; Table 26 shows its estimates for the de- mand for its kits in the coming year. Each kit contains the individual items shown in Table 27, which are listed with their base sizes in pounds. Help- You, for example, can buy packs of Acetaminophen extra-strength caplets. Each pack con- tains 12 tablets and costs Help You $1.50. Help-you buys the individual items and then as- sembles kits based on the requirements for each part in each kit as shown in Table 28. These are minimum requirements in that the cus- tomer expects at least the listed quantity of each item in each specific kit. For example, in the kit for campers, there must be at least four blankets and at least three cold units (six cold packs) as well as the other items. There are two strategies available for assembly of the kits: In direct assembly, the exact requirements are put into each kit. In modular assembly, one or more standard mod- ules are developed that can be assembled and com- bined into a kit with enough modules so that the minimum requirements for each item are met. A graphic of the approach is detailed in Figure 5. If you design a module, for example, that has two units of Band-Aids (as well as the other items) and place three of these modules in a scouting kit, then the kit will have 3*2 = 6 units of Band-Aids; this will meet the requirement of four units of Band-Aids for scouting kits. In this example, there is an "overage" of two extra units of Band-Aids that costs 2* $i per unit = $2 per cach scout kit demanded. Also, the total unit con- tent in a module cannot weigh more than 15 pounds (an assembly requirement). Direct assembly meets requirements exactly, al- though it usually has higher labor costs than modular assembly. For storing inventory, modules are easier to use because they tend to be smaller than kits. Develop a strategy for modular assembly. The key costs of the modular system are the overages that oc- cur. Your strategy must include the following: the number of modules you are designing the more modules you have, the closer you can match re- quirements exactly, although the higher the costs for assembly and inventory); the unit content of each module designed; and an estimate for the total number of each module required. Your analysis should consider issues such as: the trade-off between the number of different mod- ules designed and the total overage cost (you do not need to try more than five different modules why?); TABLE 26 Kit Demand Type Number of Kits Sold Cars Hikers Campers Sports teams Scouting groups 1,000 800 100 200 300 Cost (5) Base Unit Weight (Lb.) 0.20 0.20 4 TABLE 27 Item Cost and Base Size Item Adhesive Band-Aids Ace bandages Flares Blankets Adhesive tape Cold packs Sunburn cream Antiseptic cream Acetaminophen extra-strength caplets Rubber gloves Base Unit 10 per pack 1 bandage 3 per pack 1 blanket I roll 2 per pack 1 tube I tube 12 tablets 2.50 4 1.00 2.00 0.40 0.80 0.40 0.50 0.30 3.50 1.50 1.50 3 pairs 0.20 TABLE 28 Item to Kit Requirements (Base Units) Kit Hem Sports Teams Scouting Groups Cars 1 Hikers 2 Campors 4 1-ON Ace bandages Band-Aids Flares Blankets Adhesive tape Cold packs Sunburn cream Antiseptic cream Acetaminophen caplets Rubber gloves 2 2 2 2 - -MMM - - - FIGURE 5 Modular Assembly Hiker Camping Sports Scouts Modules Band-Aids Gloves Ace bandage Tape Flares Blankels the sensitivity of your solution to the kit demand estimates (for example, what happens to your rec- ommendations if the number of scouting kits sold changes by 20%?); the sensitivity of your recommendations to the unit cost values; the sensitivity of your recommendations to the weight limit on the size of each module; and discussion about your confidence that you have the optimal solution in light of what you have covered concerning convex functions and sets