Congratulations! You are one of the select few that have received an invitation from the Famous Mr. Bako to be a part of his high energy design team! Mr. Bako is getting ready to introduce two new exciting candy products to the world! With your strong engineering prowess, you will help Mr. Bako create package designs that will influence people all around the globe to purchase his new fantastic candy products.
Mr. Bako is going to introduce his first product at the start of the new year. He is hoping this candy will revolutionize the candy industry with its three amazing flavors and fruit-filled centers. The candy will be in the shapes of little cubes and will be named “Cubets.” Cubets will be sold and packaged in two different quantities. The “Cubets Grande” and “Cubets PS” will be packaged in the shape of rectangular prisms. This is where Mr. Bako will need your ingenuity and mathematical skills. Hope you are up for the task!
Mr. Bako has created a candy empire and is well known all over the world. He did not become the leader in the candy industry without knowing how to be a smart businessman. He is known for being frugal and he does not like wasting his precious money. A major part of this design is that he wants it to be cost effective. He wants the product to sell but he wants to save every possible penny he can.
The “Cubets Grande” will be sold with 24 Cubets in each package. Find all the ways 24 Cubets can be arranged into a rectangular prism. Make a sketch of each arrangement. Record the dimensions, volume and surface area in the table provided in your student companion.
The “Cubets PS” will be sold with 12 Cubets in each package. Find all the ways 12 Cubets can be arranged into a rectangular prism. Make a sketch of each arrangement. Record the dimensions, volume and surface area in the table provided in your student companion.
Mr. Bako really wanted the “Cubets Grande” to be packaged with 27 Cubets. Why would Mr. Bako want the “Cubets Grande” to come packaged with 27 Cubets? What could be a possible explanation on why he ultimately decided to package the “Cubets Grande” in packs of 24 instead of 27? Explain your reasoning.
Mr. Bako wants you to design the wrapper for the “Cubets PS.” As mentioned before, he wants the package design to be cost-effective, but he does want the product to sell.
Based on your findings what do you think the dimensions should be for packaging the “Cubets PS”? Please defend your selection. Your choice does not necessarily have to be the cheapest, but it has to be designed to sell and sell a lot of Cubets all over the world!
If it costs $0.0001 per square unit to manufacture the “Cubets PS” wrapping, what would be the unit cost for the wrapping one package of “Cubets PS?"
If the plan is to initially manufacture 10^7 (10 to the seventh power) packages of “Cubets PS,” what would be the total cost for the wrapping alone?
Once you have selected which wrapper should be utilized and the cost has been calculated, construct the net that will be used to package the “Cubets PS.”