A poster must have 32 sq. in, of printed matter with margins of 4" each at the top and 2" at each side. Find the dimensions of the whole poster if its area is maximum.

Q: An open box will be made by cutting a square from each corner a 5-ft by 8-ft piece of cardboard and…

A:

Q: Find the dimensions of a rectangle with area 1000m2 whoseperimeter is as small as possible.

A:

Q: Find the dimensions of a rectangle with perimeter 68 m whose area is as large as possible. Show…

A: Given:Perimeter of a rectangle is 68 m.

Q: What is the longest dimension of an open top rectangular box of greatest volume that can be…

A:

Q: Find the dimensions of the rectangular corral split into 2 pens of the same size producing the…

A:

Q: An open box will be made by cutting asquare from each corner of a 3-ft by 8-ft piece of cardboard…

A: Consider the "x" represent the side length of the cut-out square.  The length is 8 ft and the…

Q: A box with a square base with side length b and height h and with an open top must have a volume of…

A:

Q: Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of…

A:

Q: if an open box is to be made using a square sheet of tin, 20 inches by 20 inches, by cutting a…

A:

Q: The rectangular bird sanctuary with one side along a straight river is to be constructed so that it…

A:

Q: A farmer uses 2000 feet of fence to enclose a rectangular region and also to subdivide the region…

A: Let the width of the fence be:  w Let the length of the fence be:  l

Q: Find the dimensions of the rectangular corral split into 2 pens of the same size producing the…

A:

Q: Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of…

A: Let h is the dimension  of the square which are being cut at each corner of the cardboard, so The…

Q: Find the maximum volume of a cylindrical soda can such that the sum of its height and its…

A: we have to find the maximum volume of a cylindrical soda can such that the sum of its height and its…

Q: composed

A:

Q: What are the dimensions of a rectangular wall that can be constructed with 81 feet of brick that…

A:

Q: An open box is to be made from a 6 ft by 16 ft reetangulas card board by cutting out equaL squares…

A:

Q: Find the dimensions of the rectangle with max area that can be inscribed in a circle of radius 10.

A: Find the dimensions of the rectangle with max area that can be inscribed in a circle of radius 10.

Q: An open box is made from a 16 inch by 16 inch piece of cardboard by cutting equal squares from each…

A: This question is based on application of derivative.

Q: a publisher wants to print a book whose pages are each to have an area of 96in2. The margins are to…

A: First we have to draw a well labelled diagram.

Q: With a rectangular piece of metal 150cm by 200cm, cut out squares from each corner in order to…

A: I use second derivative method to find dimensions of box where volume maximum

Q: What is the maximum volume of a square pyramid that can fit inside a cube with a side length of 14…

A:

Q: A box with an open top is to be constructed from a square piece of cardboard 2m inches wide, by…

A:

Q: A closed box with square base and vertical sides is to be made from 150 square feet of cardboard.…

A:

Q: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides…

A: Given  Total length of the fence=2500 m Letl=length of the plotb=width of the plot

Q: 1. Find the dimensions of the rectangular corral producing the greatest enclosed area split into 3…

A: Given query is to find the dimensions of the rectangular corral

Q: The maximum possible volume of a rectangular box with the sum of its twelve edges 60 cm is

A: Given 12 edges sum is 60, let C=60So, 4x+4y+4z=CV=xyz    =xy(14C-x-y)    =14Cxy-x2y-xy2 for x>0,…

Q: A poster is to contain 300 cm? of printed matter with margins of 10 cm at the the top and bottom and…

A: Assume some variable to be length and breadth of the poster then find its area. Derivative of area…

Q: Find the dimensions of the right circular cylinder of greatest volum that can be inscribed in a…

A: Given query is to find the dimensions of a right circular cylinder that can be fit inside a sphere…

Q: A box with a square base with side length b and height h and with an open top must have a volume of…

A: Question is solved.

Q: from a piece of cardboard that is 24 cm by 48 cm ,cut equal squares out of the corners . fold up the…

A:

Q: A poster of area 6000 cm2 has blank margins of 10 cm wide on the top and bottom and 6 cm wide on the…

A: SOLUTION-

Q: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides…

A: Given length of wire is 700 m. rectangular plot's three sides are bounded by electric fence.

Q: We have 36ft2 of material to build a box of maximum volume with a square base and no top. What is…

A: To find the dimension of the square base for the optimum volume

Q: A poster must have 32 sq. in with margins of 4" each at t side. Find the dimensions o"

A: Given: A poster must have 32 sq. in. of printed matter.

Q: Find the dimensions of a rectangle with area 1000m2 whose perimeter is as small as possible.

A:

Q: A box with an open top and square base is to be created with a surface area of 300 square inches.…

A: The box is open  And base is square  Let square sides l = b = x in And height  =h in

Q: Suppose that a pentagon is composed of a rectangle topped by an isosceles triangle. If the length of…

A: We have to find the maximum area.

Q: A piece of wiren 10 m long is cut into two pieces. One piece is bent into a square and the other is…

A: Length of the wire is 10 m. Let the length used for the square be x. Thus, the length used for…

Q: Find the dimensions of the rectangle of greatest area that can be inscribed in a circle of radius a.

A: Let x and y be the length and width of the rectangle inscribe in a circle of radius a. Then the…

Q: If the length of three sides of a trapezium other than the base are equal to 10cm, then find the…

A:

Q: Find the maximum volume of a rectangular box whose surface area is 1600 cm? and whose total edge…

A: By using lagrange multiplier

Q: If an open box is made from a metal sheet 33 in. by 33 in. square by cutting out identical squares…

A: Given information: The length of the square is 33 inches that has been transformed to cuboidal box…

Q: A poster must have 32 sq. in. of printed matter with margins of 4” each at the top and 2” at each…

A:

Q: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides…

A: Let a and b be the sides of a retangular fence.

Q: Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of…

A:

Q: A rectangular building is to be built on a triangular corner lot with the perpendicular sides equal…

A: Given A rectangular building is to be built on a triangular corner lot with the perpendicular sides…

Q: An open topped box is to be made from a rectangular piece of metal 18cm x 48 cm by cutting off…

A: