HOMEWORK 5 – TUAN NGUYEN The goal of the United Air Cleaner Company (UACC) is to ship as many air cleaners as

possible and with the lowest cost per unit. Based on the data of provided, the packaging engineer can estimate the cost per unit of each packaging systems and recommend the best packaging method to the company.

Let's start by examining the single use system. The maximum pallets that will fit in one layer of the truck is 16 (because of clearance restriction there will be 2 pallets in the cross truck direction (40'' wide), and 8 pallets in the lengthwise direction). The maximum boxes that will fit in one layer of the pallet is 6. The weight of a pallet with 1 layer is 254 lb, with 2 layers is 458 lb, and with 3 layers is 662 lb. The height of the pallet with one layer is: 26.75”, the height of the pallet with two layers is 46.5”, the height of the pallet with three layers is 66.25”. We can either put 16 pallets loaded with 3 layers or 32 pallets loaded with 2 layers each to the truck. The weight of the loaded pallets will be 10592 lb, or 14656 lb respectively, which are over the capacity of the truck. Therefore, the truck load is limited by the weight. The number of the pallets loaded with filters in corrugated boxes can be loaded onto the truck when the filters are stacked in 1 layers on the pallets in the single use system is (5000/254) = 9, for 2 layers the number is 10 and for 3 layers the number is 7. It is best to use a pallets with 3 layers because it gives the greatest number of filters per truck: (3 layers/pallet) * (7 pallets) * (6 filters/layer) = 126 filters. The total cost of boxes, pallets, and truck for 1 trip from UACC to BTMC is:

(126 boxes* $2.5/box) + (7 pallets $20 /pallet) + (325 miles* $1.85/mile) = $1056If we use the single use system we can ship 126 filters in one trip and the cost per filter is $8.38.

Now we examine the reusable packaging system. The width of the truck is 96”, however, the width of two reusable containers are 96” plus we have the clearance restriction of 1” between adjacent containers and between containers and the sides of the truck we can only have one container in the cross truck direction at a time. This enable us to calculate the number of containers that will fit in the truck to be 8 containers (390”/48”=8.125). We can fit 9 filters on a layer in a reusable container. Because the filters are not stackable, there is only one layer per container. The weight per loaded container will be: 9*32 + 115 = 403 lb. Unlike the filters which are unstackable, the reusable container can be stackable that enable the maximum containers fit into a truck to be 16. However, due to weight restriction the number of containers in the truck will be: 12 containers (5000 lb/403 lb/container = 12.4). The maximum number of filters per truck will be 12*9 = 108. The number of collapsed containers can be loaded onto one of the trucks for the return trip to the UACC plant is 8*2*8 = 128 (if the clearance restriction is ignored). The number of loaded trips will be made to accumulate the containers for the first return trip is 128/12 = 10.66. The cost per trip would be:

12 containers * ($145 containers/15) + (325 mile*$1.85/mile) + (325 miles*$1.85/mile)/10.66 = $774(The container can be used 15 times so the cost will be divided by 15.)The cost per filter will be: $7.2 if we use the reusable containers.The the best way is to use the reusable containers. However if we use the reusable containers, the filters/trip would be a little bit lower. If the number of trucks are limited, this should slow down production a little bit.