Maximum-volume box Suppose an airline policy states that allbaggage must be box-shaped with a sum of length, width, andheight not exceeding 108 in. What are the dimensions and volumeof a square-based box with the greatest volume under these conditions?

Q: An isosceles triangle is inscribed in a circle of radius R. Find the value of 0 that maximizes the…

A: In this question we have to find which option is good.

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 rectangular tank with a square base, an open top, and a volume of 32ft^3 is to be constructed of…

A: Let side of square base be x ft and height be y ft Given, Volume=32 ft3 X2y = 32, y = 32/x2 – i)…

Q: A certain airline requires that rectangular packages carried on an airplane by passengers be such…

A: According to the problem, we have

Q: 10. A rectangular box is to be made from 16m2 of cardboard. Use Lagrange multi- pliers to find the…

A: (10) Consider the provided question, Give that, rectangular box has to be made from 16 m2 cardboard.…

Q: A certain airline requires that rectangular packages carried on an airplane by passengers be such…

A:

Q: A can of Monster has a height of 15.9 cm, a radius of 3.3 cm, a circumference of 20.7 cm, and a…

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Q: 2) The volume of an open box with a square base is 4,000 cubic centimeter (cc). Find the dimensions…

A: The volume of an open box with a square base is 4,000 cubic cm.

Q: 17. Maximizing volume. From a thin piece of cardboard 20 in. by 20 in., square corners are cut out…

A: Dimensions of a thin piece of cardboard is 20 in. by 20 in. Let x in. be cut out from each corner of…

Q: A box with an open top has vertical sides, a square bottom, and a volume of 4 cubic meters. If the…

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Q: 3. A rectangular page is to contain 36 square inches of print. The margins on each side are to be 1…

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Q: Circle in a triangle What are the radius and area of the circle ofmaximum area that can be inscribed…

A: Given Data The two equal sides of the isosceles triangle is a=b=1.   Consider the third side of the…

Q: 20. Minimizing surface area. Drum Tight Containers is designing an open-top, square-based,…

A: Volume of a cuboid is lbh. Since it is mentioned that it is square-based so l=b. l2h=62.5 in3…

Q: open rectangular box with square base is to be made from 48 ft2 of material.  What dimensions will…

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Q: A box with an open top has vertical sides, a square bottom, and a volume of 256 cubic meters. If the…

A: Solution: Let x is the base of the box Let y is the width of the box Let z is the height of the box…

Q: A certain airline requires that rectangular packages carried on an airplane by passengers be such…

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Q: 47. Minimum material. A rectangular box with no top and two parallel partitions (see the figure)…

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Q: 10. An open box is to be made by cutting a square from each corner of a 12-inch-by-12-inch piece of…

A: Suppose the side of the square to be cut off from each corner is "x" inch. Therefore, the length of…

Q: 8. Arectangular field is to be bounded by a fence on three sides and by a straight stream on the…

A: Let be the length of the side parallel to the stream and let be the length of the side…

Q: A certain airline requires that rectangular packages carried on an airplane by passengers be such…

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Q: 21. Minimizing surface area. An oil drum of standard size has a volume of 200 gal, or 27 ft³. What…

A: Let the radius of the drum be rft and height be hft. As the volume of the drum is 27ft We get…

Q: 6. A new shed is going to be built. The volume of the shed must be 240 cubic feet. Determine…

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Q: A rectangular tank with a square base, an open top, and a volume of 10,976 ft is to be constructed…

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Q: b) Maximize the volume of this rectangular box. c) What are the dimensions & volume of this largest…

A: Solved below.

Q: An open box (no top) is to be made by cutting congruent squares from each corner of a 12-inch by…

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Q: An open cardboard box is to be made with a volume of 4m'. Find the dimension of the box that…

A: Volume has given, we use surface area of cardboard to solve following question

Q: A rectangular tank with a square base, an open top, and a volume of 27,436 ft is to be constructed…

A: Given: - A rectangular tank with a square base, an open-top, and a volume of 27436ft3 is to be…

Q: A certain airline requires that rectangular packages carried on an airplane by passengers be such…

A:

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: 1. (. A box is to be made from a rectangular sheet of paper by cutting out squares from the corners…

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Q: 8. A rectangular box with no top is to be made from a piece of cardboard that is 20 ft by 20 ft.…

A: Dimension of cardboard=20ft by 20ft

Q: 3. From a thin piece of cardboard 14 in by 14 in, square corners are cut out so that the sides can…

A: This question can be solved using the concept of maxima and minima.

Q: 1. A dairy farmer plans to enclose a rectangular pasture adjacent to a river. The pasture must…

A: We will use general knowledge of arithmetic to solve this question.

Q: 1. The volume of an open box with a square base is 4000 cm3. Find the dimensions of the box if the…

A: There are multiple question, As per company policy ask other question separately.  assume  side of…

Q: Squares with sides of length x are cut out of each corner of a square piece of cardboard with sides…

A: Length of the box, l=L-2xWidth of the box, w=L-2xHeight of the box, h=x Volume of the box, Vx=lwh⇒…

Q: An open box is to be made out of a 6-inch by 14-inch piece of cardboard by cutting out squares of…

A: Cardboard with x2area cutouts is  Volume of the box , V = l w h cu.units Where length = 14 -2 x…

Q: A rectangular box with an open top and one partition is to be constructed from 288 square inches of…

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Q: 5. An open box of maximum volume is to be made from a square piece of material, 24 inches on a side,…

A: 5 Sol:length of box = 24-2x=lwidth of box = 24-2x=wheight of box =x=hthe volume, V = (24-2x) x…

Q: A company plans to manufacture a rectangular container with a square base, an open top, and a volume…

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Q: 24. An open box is to be made by cutting a square from each corner of a 20-cm-by-32-cm piece of…

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Q: Find the dimensions of the rectangle of maximum area that can be inscribed in a circle of radius  r…

A: To find the dimensions of the rectangle

Q: An open box is to be made out of a 12-inch by 14-inch piece of cardboard by cutting out squares of…

A: Given: The size of cardboard is 12-inch by 14-inch  To find the dimension of the resulting box that…

Q: 1. An open-top box with a square base is made from a cardboard of area 75 cm². Find the maximum…

A: given area is 75cm2find the maximum volume of the box

Q: A rectangular solid with a square base has a surface area of 121.5 square centimeters. (Let w…

A: Let w represent the width of the sides of the square base and h represent the height of the…

Q: square corners are cut out so that the sides can be folded up to make a box. What dimensions will…

A:

Q: 9. If 1200 square centimeters of material is available to make a box with a square base and an open…

A: Use second derivative test

Q: An open cardboard box is to be made with a volume of 4m. Find the dimension of the box that requires…

A:

Q: Determine the page dimensions that will result in the maximum printed area on the page

A: Assume that the length of the page be x and width be y. Since area of the page is 50 square inches,…

Q: 8) A farmer wishes to enclose a rectangular area on three sides along a stream. The area needed for…

A: Let x is length and y width

Q: A box with an open top has vertical sides, a square bottom, and a volume of 4 cubic meters. If the…

A: Given: Volume = 4 m3