(Optimization) A closed cylindrical storage drum is to be made with a volume of 16 ft3. What are the dimensions of the cylinder that will require the least amount of material to construct?

Q: The following diagram shows two cylindrical teapots. The yellow teapot (big) has the same diameter…

A: Since the yellow teapot has same diameter as that of green teapot but is one and half time tall wrt…

Q: A cylindrical can has a volume of 2000r cm°. What dimensions yield the minimum surface area? The…

A: A cylindrical  can has a volume of To find: Dimensions that yield the minimum surface area and the…

Q: Optimization An open-top rectangular box is to have a square base and a surface area of 100 cm2.…

A: Given: Surface area of an open top rectangular box = 100 cm2. To find: We have to find the…

Q: A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 550…

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Q: You want to design a box with a square base such that the sum of its length, width and height does…

A: Length , bredth and height all must be equal to 12 cm  Hence total volume will be 1728 cm^3

Q: Help the students determine the dimensions of the can that will minimize the cost of the materials…

A: Above question is solved.

Q: The following diagram shows two cylindrical teapots. The yellow teapot (big) has the same diameter…

A: From the given information, the two tea pots has same diameter and the yellow teapot is one and…

Q: BONUS: Use Lagrange multipliers to find the dimensions of the box with largest volume possible and…

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Q: 40 30 20 10 -10 10 20 30 40 50 60 10 You are a lifeguard and spot a drowning child 60 meters along…

A: We will get an equation for a time in terms of x. We find derivative of it and equate it to 0. We…

Q: A cylindrical can is to be made to hold a volume of 10 ft and the the least amount of metal. See…

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Q: You are making a rectangular box with a square base and an open top. Its volume must be 4 ft^3. Find…

A: Let the length of a side of the base= x Height = y So, volume= x2y=4  Or, y=4/x2   Surface area:…

Q: Design the optimal cylindrical container that is open at one end and has walls of negligible…

A: Given: A cylindrical container which is open at one end and has walls of negligible thickness The…

Q: You need to construct a cylindrical container with a circular base and no top, having a total…

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Q: aving 3m2 of aluminu

A: Given Having 3m2 of aluminum foil at your disposal, you want to build a rectangular box with a lid,…

Q: A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 550…

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Q: EXERCISES A. A box with a square base and open top must have a volume of 256 cm Fimd the dimensions…

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Q: A closed cylindrical can is to have a surface area of 8 square units. Show that the can of maximum…

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Q: Minimizing Packaging Costs A rectangular box is to have a square base and a volume of 63 ft. If the…

A: Lagrange multiplier

Q: An open-top rectangular box is being constructed to hold a volume of 200 in. The base of the box is…

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Q: A farmer plans to fence three rectangular pastures adjacent to a river. The pastures must contain…

A: Let x be the length and y be the width of the rectangular land.Since the land covers an area of…

Q: 10. rectangular box with a square base and open top must have a volume of 4 m³. Find the dimensions…

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Q: 2. A cylindrical can is to have a volume of 20 cm³. Find the radius and height of the can that will…

A: The second derivative test : Let f(x) be the given function and she be the critical point of f. If…

Q: The following diagram shows two cylindrical teapots. The yellow teapot (big) has the same diameter…

A: The volume of a solid is defined as how much space a object takes up. It is measured by number of…

Q: A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 1650…

A: Given:   V = 1650  styrofoam costing 0.02 cents per square centimeter. costing 0.09 cents per square…

Q: A farmer plans to enclose a 200 ft^2 rectangular field that borders a straight river. He needs no…

A: The solution is given in the next steps.

Q: A microwaveable cup-of-soup package needs to be constructed in the shape of a cylinder to hold 450…

A: Volume of soup to be held in container V = 450 cm3 Cost of styrofoam = 0.02 cents/cm2 Cost of glued…

Q: A closed cylindrical container has a surface area of 400cm². Determine the dimensions for maximum…

A: A function will have a maximum at a point where the value of the first derivative of the function…

Q: You have decided to build a fish tank to keep piranhas. The rectangular base and four sides will be…

A: Given:-  The rectangular base and four sides will be made of shatterproof glass costing R800 per…

Q: You have been asked to design a rectangular box with a square base and an open top. The volume of…

A: See this solution in below

Q: A rectangular storage tank with an open top is to have volume (20 m). The length of the base is…

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Q: A farmer wants to build a rectangular fence that will enclose 120 square feet for his dog Miff. The…

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Q: A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 250…

A: Given that a microwaveable cup-of-soup packages needs to constructed in the shape of cylinder to…

Q: A rectangular base box must be constructed, with a sheet of cardboard 40 cm wide and 50 cm long,…

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Q: A manufacturer of transparent container makes a plastic cylindrical aquarium

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Q: Equal squares are cut from the corners of a cardboard, 16 cm wide and 30 cm long. an open box is…

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Q: Waste Management Company wants to construct a dumpster in the shape of a rectangular solid with no…

A: Consider the given information:

Q: A manufacturer needs to make a cylindrical can that will hold 1500 cubic centimeters of liquid.…

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Q: container. We have 550 cm2 of metal. What dimensions would maximize the volume of the container?…

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Q: An aluminum can needs to be constructed which can hold 20T cm3 The cost of aluminum is $10 per…

A: Given  Volume of can is 20π cm³ Cost for top and bottom = 10$/cm Cost for lateral surface = 8$/cm…

Q: You have been asked to design a rectangular box with a square base and an open top. The volume of…

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Q: The base and sides of a container is made of wood panels. The container does not have a lid. The…

A: Given, The volume of the wooden cuboidal container with width x cm and length five times its width =…

Q: MY NOTES ASK YOUR TEACHER A rectangular box is to have a square base and a volume of 20 ft. If the…

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Q: You are making a rectangular box with a square base. Its volume must be 8 ft^3 . Find the dimensions…

A: A rectangular box with a square base. Its volume must be 8 ft3

Q: A storage shed is to be built in the shape of a box with a square base. It is to have a volume of…

A: A storage shed is to be built in the shape of a box with a square base. It is to have a volume of…

Q: A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 250…

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Q: Rectangular boxes with a volume of 8 m³ are to be made of three materials. The material for the top…

A: Let the dimensions of the box be x,y, and z. Given the volume of the rectangular box is xyz=8. Let…

Q: You are designing a glass candle holder.  It will be a rectangular prism with outer surface area 200…

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Q: The surface area of an open-top cylindrical box is 27π cm ². Determine the dimensions of the…

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Q: Minimizing Packaging Costs A rectangular box is to have a square base and a volume of 45 ft. If the…

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Q: We want to construct a box whose base length is three times the base width. The material used to…

A: Here we want to construct a box whose base length is three times the base width. The material used…