Top Class Posters

Calculus optimization problems, please answer it serious, doesn’t matter if it is wrong, 10 points for sure?

1(a) set up and solve the optimization for the minimum materials to make a cylinder to hold 355 ml of pop

a)Taking the radius=r and the height to be h

The amount of material = surface area=S

S=2*pi*r^2 + 2*pi*r*h

We know the volume is 355
Equation for volume=pi*r^2*h

so

355=pi*r^2*h
This allows us to get rid of one of our variables
h=355/(pi*r^2)

Substituting back into our equation for surface area:
S=2*pi*r^2 + 2*pi*r*355/(pi*r^2)
S=2*pi*r^2 + 710/r

To minimise find dS/dr = 4*pi*r – 710/r^2 = 0
4*pi*r^3=710

r=3.837 cm (substitute back)
h=7.675 cm

ie height twice radius

b)result squatter and fatter than the actual can. result accurate – real coke cans waste material.

c)optimised can would be difficult to hold – real can has smaller radius

d)size of seams. also how many can stack on a shelf

OXO 12 pc. TOP Container Set 7705889

Norpro 431 4-Piece Silicone Ice Pop Maker Set $11.99 Create your own pop treats. Easy to push up with this cleaver design. Set of 4 . Lid holds in ingredients before they freeze and keeps pops secure in ice chest for picnics and BBQ’s. Fill seal freeze and enjoy. Create treats using juices, purees, yogurt, soda, ice cream, pudding, applesauce, gelatin, fruit, berries, candies, chocolate, carmel, whipped cream and sprinkles!…

Tovolo Groovy Ice Pop Molds, Set of 6 …

Tovolo Star Ice Pop Mold …

Zevro MSR1400 Zero Gravity Magnetic Spice Rack with 12 Canisters $29.69 With its sleek, modern-looking design, this wall-mountable magnetic spice rack keeps spices within easy reach while saving on counter space. The unit provides 12 plastic spice canisters, each holding up to 1-3/4 ounces of anything from cinnamon, allspice, and nutmeg to chili power, garlic powder, and basil (spices not included). Adjust the lids–from closed to sprinkle or pour–with a nudge of the…

Rubbermaid FG1A52RD Salt and Pepper Shaker $3.79 Salt & Pepper Shakers, Great For Storing, Snap Tight Lids, Seal Keeps Contents Dry, Dishwasher Safe….

Household Essentials 5503 Magic Storage Cube, 3-Pack Breathable and collapsible, these Magic Cube storage boxes from Whitney Design are the ultimate tool for occasional storage. They are suitable for light- to mid-weight items, such as files, toys, laundry, or extra blankets by the guest bed. Designed to pop gently open into position, the cubes feature durable plastic inserts and edge framing, breathable canvas fabric, and reinforced carrying handle…

Popcorn Paper Bag $3.29 Popcorn Party Bags! We have the party supplies you need to make your event a hit! These Popcorn party bags are just what you need to pass out popcorn at your event. A dozen bags per package. 10″ long, 5″ wide and 3 1/4″ deep. Great for popcorn at carnivals as well as goodies and gifts. Use this Popcorn bag to pass out popcorn at your event. You can’t go wrong with party bags from Century Novelty. …

Apex Weekly Pill Organizer, Twice-a-Day, 1 Pill Organizer (Colors May Vary) $1.96 If you are taking medication at two times every day, this is the organizer for you. Easy to read and manipulate, the Twice-a-day Weekly Pill Organizer will simplify your complicated life….

Huggies Natural Care Baby Wipes, Unscented – 16 ea $1.09 INDICATIONS: Huggies Natural Care Baby Wipes Fragrance Free use Alcohol free, Keep lid tightly closed. INGREDIENTS: Huggies Natural Care Baby Wipes Fragrance Free contains Water….

Art of Appreciation Gift Baskets Concession Stand Popcorn & Candy Gift Set $19.99 Movie buffs will applaud this classic candy and popcorn snack sampler – it’s just like taking a trip to the theaters concession stand for snacks to enjoy with your favorite movie! Presented in a reusable popcorn container, they’ll enjoy 2 packs of buttery Movie Time Popcorn, Movie Bag of Gummi Treats, Jelly Belly Popcorn Jelly Beans, Skittles, Sweet Tarts and of course, every movie buff needs a pa…