Chicago, Illinois, is 60 miles away from the business. 8,100 identical lights were to be designed by it and shipped to China in a 40-foot container. The container has the following measurements: 40 feet long, 8 feet wide, and 8.5 high. The conditions stipulated included shipping the container containing the lamps to Shanghai's port. The business chose to create prototypes in three distinct styles, designated Style A, B, and C. Here are the details of the various style, in terms of sizes, shapes, weights, costs, carton meant to contain them, and the weight of the container as well. We are to calculate the number of lamp shades, of each style, that are to be loaded in to a 40 – foot container to be transported to Shanghai, China.
Style A
Cylindrical in shape, 11inch height and 11-inch diameter, packed in a 12 by 12 by 12inch carton. The weight of the cylinder is 9lb and the carton 1lb totalling to 10lb. Cost of designing each of this cylinder type is $4 and the carton is 60cts.
Solution:
We are to determine the volume of the carton and that of the container in square foot, since that is what will be loaded in the 40 – foot container. We convert inch to foot first.
1 inch = 0.0833 feet
Therefore 12 inches = 12 X 0.0833 = 0.9996 feet
0.9996 X 0.9996 X 0.9996 = 0.9988 FT3
Container volume is 40 X 8 X 8.5 = 2720 FT3
We divide the container volume by that of the carton to get how many cartons can fit in the container.
2720/0.9988 = 2723.27 rounded off to the nearest whole number, we get 2723 cartons. With each carton carrying one lamp shade, we have 2723 shades in the container.
Style B
Conical in shape, with the same diameter and height, 11inch (assumptions), packed and nested into 6 lampshades, in a carton of 12 width by 12 lengths by 40 inches high, which has a weight of 62lb. cost of a lampshade is $4.5 and that of the carton is $2.
Solution
1 inch = 0.0833 feet
12 inches (as found above) is 0.9996 feet
40 inches is 40 X 0.0833 = 3.332 feet
Volume of the carton is 0.9996 X 0.9996 X 3.332 = 3.3293FT3
Volume of the 40 – container, as calculated earlier is 2720FT3
Diving the two values, volumes, we get; 2720/3.3293 = 816.989 rounded off to 817 cartons.
And each carton has 6 lampshades, so 817 cartons will have 817 X 6 = 4902 lampshades
Style C
This has the same shape as style B, but is nested in 10 lampshades in a carton of 12 by 12 by 48 inches. The weight is 101lb, together with the lampshade, cost of $5 per lampshade and $2.25 for the carton.
Solution
1 inch = 0.0833 feet
12 inches (as found above) is 0.9996 feet
48 inches is 48 X 0.0833 = 3.9984 feet
Volume of the carton is therefore; 0.9996 X 0.9996 X 3.9984 = 3.9952FT3
But we know the volume of the 40 – container, as 2720FT3
If we divide we get 2720/3.9984 = 680.27 rounded off as 680 cartons
But each carton, according to style C carries 10 lampshades; so, we have 680 X 10 = 6800 lampshades
Conclusion
According to the calculations above, the company will transport more lampshades considering style C than style B and C. Let There Be Light, will choose what is priority for them, delivering more lampshades at ago or looking at cost implications of delivering the lights. If they have to deliver 8,100 lampshades, then style A, B and C will take around 3, 2 and 1 & a 16th containers. In the approximations.
References
Robert Smith, 2014, The Art and Science of Packing a Shipping Container – Part 1 [Online] (updated 3 Nov. 2014) Available at: < http://www.shippingsolutions.com/blog/art-science-packing-shipping-container-1>
