A rectangular storage container with an open top is to have a volume of 10 cm^3. The length of its base is twi?
A rectangular storage container with an open top is to have a volume of 10 cm^3. The length of its base is twice the width. Material for the base cost $15 per square meter. Material for the sides costs $128 per square meter. Find the cost of the material for the cheapest such container.
Ok, We have to use the Area formula (in terms of Cost) to solve this. However, we are not given the height, so we first find the height from the volume formula. Since l = 2w and V = 10 = 0.1m^3, so,
V = 0.1 =lwh
0.1 = (2w)wh = 2w²h
h = 0.1 / 2w²
Therefore:
Cost = 2 long sides * $128 + 2 short sides * $128 + $15 * base
C = 128*2(2w*0.1 / 2w²) + 128 * 2(w * 0.1 / 2w²) + 15(2w*w)
C = 25.6/w + 12.8/w +30w², take the derivative
C ‘ = -25.6/w² – 12.8/w² + 60w, now set it equal to zero and solve for w
-25.6/w² – 12.8/w² + 60w = 0, use common denominator and then solve for w
-25.6/w² – 12.8/w² + 60w^3/w² =0
-25.6 – 12.8 + 60w^3 = 0
60w^3 = 38.4
w^3 = 0.64
w = (0.64)^(1/3)
w = 0.86177 meters
h = 0.1/(2w²)
h = 0.1 / (2 * 0.86177²)
h = 0.67326 meters
l = 2 * w = 2(0.86177)
l = 1.72355 meters
Cost = 2*l*h + 2*w*h + 15lw
Cost = 128*2(1.72355)(0.67326) + 128(2)(0.86177)(0.67326) + 15(1.72355)(0.86177)
Cost = $467.9
Therefore, the cost of the material for the cheapest such container is $467.9.
Hope this helps.
Edited: I edited the final answer from 447 to the above, because I forgot to calculate the area of the base by $15.
531 2-CAV RECTANGULAR CONTAINER TOP-ENTRY IML + PICKUP.mpg
|
|
Pyrex 6022369 Storage 14-Piece Round Set, Clear with Blue Lids $19.99 Pyrex 14-pc Storage Set ***OPEN BOX*** This NEW product you are browsing has been inspected by our certified technicians to ensure that it meets factory specifications; it is guaranteed to be in perfect working order.The Equipment is sold in AS IS condition and returns will not be accepted so please contact us with any questions BEFORE placing an order at 1-800-572-3224 Ext: 243. We ac… |
|
|
Bormioli Rocco Frigoverre Jug with Hermetic Lid #N/A… |
|
|
Pyrex 6021224 Storage 10-Piece Set, Clear with Blue Lids $14.99 Pyrex bakeware is durable, transparent for easy monitoring of baking progress and provides good heat conduction for even, consistent baking. Pyrex glass is safe in the oven, microwave, refrigerator, freezer, and dishwasher. Pyrex glass is nonporous, so it won’t absorb food odors, food flavors, or food stains. Plastic lids are great for storage in refrigerator or freezer. Includes 1 each: 3 cup rec… |
|
|
Fiskars 9405 Kangaroo 30-Gallon Gardening Container $15.76 Perfect for pruning or weeding jobs, the Fiskars Kangaroo 30-gallon gardening container holds itself open, freeing your hands for work. The Kangaroo’s unique spring design springs up to a 22-inch diameter, 30-gallon capacity, just waiting to be filled with weeds, pruned branches, or raked leaves. When you’re done, the container can be collapsed and stored easily in a compact, ready-to-hang 3-inch … |
|
|
Sterilite 19848006 18-Quart Ultra Storage Box, White Lid See-Through Base with Titanium Latches, 6-Pack $44.99 … |
|
|
Rubbermaid Commercial Soft Molded Plastic 10.25 Gallon Wastebasket, Rectangular, Black $7.10 Lightweight containers are easy to handle and fit in well in many home and work environments. Rolled rims add durability and are a breeze to clean. All-plastic construction won’t chip rust or dent. Optional lids sold separately. Waste Receptacle Type: Wastebaskets Material(s): Plastic Application: General Waste Capacity (Volume): 10.250 gal.Unit of Measure : Each… |
|
|
simplehuman Custom Fit Trash Can Liner J, 38- 40 Liters / 10- 10.5 Gallons, 50-Count $15.99 CW0170 Features: -Trash can liner.-Custom fit.-Bag stays completely hidden when lid closed.-Extra durable plastic and thick double seams prevent rips and tears.-Convenient drawstring handles for easy lifting.-Handy dispenser packs perforated opening for easy dispensing.-Capacity: 38-4 liters (1-1.5 gallon).-ISTA 3A certified…. |
|
|
simplehuman Custom Fit Trash Can Liner H, 30-35 Liters / 8-9 Gallons, 20-Count (Pack of 4) $23.96 simplehuman liners are tailored to fit cans perfectly, so the bag stays completely hidden when the lid is closed…. |
|
|
simplehuman Custom Fit Trash Can Liner C, 10-12 Liters / 2.6- 3.2 Gallons, 20-Count (Pack of 3) $14.97 simplehuman liners are tailored to fit cans perfectly, so the bag stays completely hidden when the lid is closed…. |
|
|
Silver Black Sparkle Animal Print Nested Canister Set/3 Iron $65.49 Product Summary: Decor…. |
Tags: container rectangular plastic, food, glass, kitchen, packaging, rectangular container, rectangular container gardening, rectangular glass container, rectangular plant container, storage