Question

A paper manufacturer is evaluating their packing procedures. Currently, they package twelve reams of paper in a box—in three stacks of four reams. However, their company has been getting complaints from the retail stores that the box is too large and heavy for the average consumer to carry by their self. So, they have decided to reduce the weight of each box by ten pounds. You have been asked to explore the different packing options based on the new weight condition and present your recommendation to the CEO of the paper company. Questions: 1. Identify three unique ways to package the paper given the new weight condition. Include both the dimensions of the new boxes, as well as a verbal description of how the reams will be packaged. You may include sketches if you wish. 2. Calculate the volume of each box you described in the three ways to package the reams of paper. Are you surprised by the results? Why or why not? 3. Calculate the surface area of each box you described you configured. Are you surprised by the results? Why or why not? 4. Based on your results in the other parts, write a paragraph presenting your recommendation to the CEO of the paper manufacturing company.

Use complete sentences and explain your reasoning.

Answer 1

Three unique ways to package the paper given the new weight condition are presented. Calculations for the volume and surface area of each box are provided, and a recommendation is made based on the results.

Step-by-step explanation:

Three unique ways to package the paper given the new weight condition are:

• Option 1: Package six reams of paper in a box—in two stacks of three reams. The dimensions of the new box can be 10 inches by 8 inches by 6 inches.
• Option 2: Package eight reams of paper in a box—in two stacks of four reams. The dimensions of the new box can be 12 inches by 9 inches by 8 inches.
• Option 3: Package ten reams of paper in a box—in two stacks of five reams. The dimensions of the new box can be 14 inches by 10 inches by 10 inches.

Now, let's calculate the volume and surface area of each box:

• Option 1: Volume = 10 x 8 x 6 = 480 cubic inches, Surface Area = 2(10x8) + 2(10x6) + 2(8x6) = 160 + 120 + 96 = 376 square inches.
• Option 2: Volume = 12 x 9 x 8 = 864 cubic inches, Surface Area = 2(12x9) + 2(12x8) + 2(9x8) = 216 + 192 + 144 = 552 square inches.
• Option 3: Volume = 14 x 10 x 10 = 1,400 cubic inches, Surface Area = 2(14x10) + 2(14x10) + 2(10x10) = 280 + 280 + 200 = 760 square inches.

Based on the results, Option 1 has the smallest volume and surface area, making it the most compact and efficient packing option. I recommend using Option 1 to reduce the weight of each box while maintaining a manageable size.