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Calculus
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A school cafeteria offers a lunch combo special where you get soup, a sandwich, and a drink for $4.99. There are 3 kinds of soup, 4 kinds of sandwiches, and 5 kinds of drinks. How many possible combos are there?

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Related questions

Please show work. Thank you.


Twelve Pack Container Lab Twelve packs of soda cans traditionally are sold in boxes that are either 3 rows of 4 cans standing upwards or 6 rows of 2 cans with the cans on their side.

Are there other ways to do this and what is the cost? You are to assume the role of a product-release engineer for a major soft-drink company.

Using optimization procedures involving some calculus, they would like you to come up with a container that can open and close, can carry a twelve pack of cans, but at the same time, minimizes the cost to make the container.

Materials and labor cost $0.35/cm2 and you have no restrictions on the shape of the container. Compare this with some of the “normal” containers that carry cans (6x2 upright box, 2x6 “on their side” box….)

Draft a proposal showing three possible containers with dimensions, cost, the amount of “empty” space and writing a brief "sales" pitch which you believe is the best option and why. Remember that neatness, creativity, and proofreading are always required.

Assume the following:

· Cans are cylinders with dimensions that are 12.3 cm tall and with a 6.6 cm diameter

· “Empty” Space is the volume of the container minus the volume of the 12 cans.

· The Cost of a container is the Surface Area * $0.35 per square cm.

· Container shapes are not limited to rectangular boxes…triangular pyramids, cylinders, or torus/donut shapes are other possibilities (and there may be others). This assignment is due on Monday, November 27, 2017.

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