A rectangular box of height y having a square base with sidelength x is to be made. If the area of the box is 486 units then, to maximize the volume, x must be must be units. Then the maximum volume is

Q: An open-top box is to be made from a 20 in by 30 in piece of cardboard by removing a square from…

A: Let each side of the square cut-off from each corner be x in. then the length of the base of the box…

Q: If a rectangle has dimensions x and y, then we must maximize the area A = xy. Since the perimeter is…

A:

Q: A solid steel cylinder is to be produced so that the sum of its height h and diameter 2r is to be at…

A:

Q: A closed rectangular box to contain 16 ft³ is to be made of three kinds of materials. The cost of…

A: Let's find dimension for minimum cost of given rectangular box.

Q: a. Find the radius and height of a cylindrical soda can with a volume of 256 cm that minimize the…

A: Part (a) Given data: The volume of can is V = 256 cm3.

Q: A rectangular lot is to be fenced in using two different kinds of fencing. Three sides will be…

A: Given that, Three sides of rectangular land will be fenced using standard fencing that costs $7 per…

Q: If an isosceles triangle has a fixed perimeter P, find the dimensions that maximize the area. Your…

A: Given: An isosceles triangle is given with perimeter P. The objective is to find the dimensions of…

Q: Of all numbers whose sum is 50, find the two that have the maximum product. That is, maximize Q =…

A:

Q: An open-top box is to be constructed so that its base is twice as long as it is wide. Its volume is…

A: Volume of cuboid is V=LWH Here,  L=lengthW=widthH=height Surface area of cuboid with open top is…

Q: A company sells chocolate in rectangular boxes whose volume is 120cm^3. For display purposes, the…

A: Given that the volume of rectangular boxes is 120cm . Then length of the box is three times the…

Q: A farmer has 1700 m of fencing and wishes to enclose a rectangular area and then divide it into 5…

A:

Q: A wire of length 10 is to be cut into two pieces, one being bent to form a square and the other to…

A:

Q: A piece of 1m wire is cut into two parts, one bent into the shape of a circle and the other into the…

A:

Q: 2. Helmut, an ostrich farmer, wants to build a rectangular fenced enclosure divided into five…

A: Given that, Total length= 120 m

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 for electric fencing is 2000 m, and one side of plot is bounded by a river. To…

Q: A rectangular sheet of metal having dimensions 20cm by 12cm has squares removed from each of the…

A: A rectangular sheet of metal having dimensions 20cm by 12cm has squares removed from each of the…

Q: A rectangular silo with open top and has a square base for food storage is a school project of two…

A: We will use the basic knowledge of formulas of surface area and volume of cuboid, and the knowledge…

Q: A rectangular box of height y having a square base with sidelength x is to be made. If the area of…

A:

Q: A company plans to manufacture closed rectangular boxes that have volume 24 cubic feet. The cost per…

A:

Q: A closed rectangular box is to be constructed with a base that is twice as long as it is wide. If…

A:

Q: A box with a rectangular base is to be constructed of material costing $2/square inches for the…

A: Given problem is : A box with a rectangular base is to be constructed of material costing $2/square…

Q: A customer has made a request for a wooden box with an open top that needs to have a volume of…

A: Note:- As per your demand we solve it for only constraints for this optimization  Given problem:- A…

Q: We want to construct a box with a square base and we only have 10 m² of material to use in…

A:

Q: 2. Find the length and width of a rectangle that has an area of 800 square feet and whose perimeter…

A:

Q: a rectangular box without lid is to be made from a square cardboard of sides 18cm by cutting equal…

A:

Q: A box with no top and a square base has to be designed so that its volume must 108 cm³. Find the…

A:

Q: Two chicken coops are to be built adjacent to one another using 120 ft of fencing. a. What…

A: Total fence needed is: (x+x+x)+y+y+y+y=3x+4y So, 3x+4y=120

Q: A rectangular lot is to be fenced in using two different kinds of fencing. Three sides will be…

A:

Q: A box with a volume of 530 cm3530 cm3 is to be constructed. The sides of the box cost 3 cents per…

A: Given, Volume of the box = 530 cm3 Sides of the box cost = 3 cents/cm2 Top and bottom cost = 6…

Q: A farmer wishes to build a rectangular fence and has 800 meters of fencing material with which to…

A:

Q: A box with an open top is to be constructed from a square piece of cardboard that is 4 feet wide by…

A: Square piece of cardboard of 4 feet wide. Let x feet be cut off from each corner of the square piece…

Q: . A decorator, who is a monopolist, makes two types of specialty picture frames. From experience,…

A:

Q: Suppose a farmer wants to fence off a rectangular field alongside a river with a total area of 15,…

A: Given, Area= 15000m2 we draw a diagram according to the question we have to find the dimension of…

Q: A rectangular box without lid is to be made from a square cardboard of sides 18 cm by cutting equal…

A: This question is based on application of derivative.

Q: A poster is to contain 300 cm2 of printed matter with margins of 10 cm at the the top and bottom and…

A: We have, A poster is to contain 300 cm2 of printed matter with margins of 10 cm at the the top and…

Q: A box with a square base and open top must have a volume of 32000 cm³. Find the dimensions of the…

A: To find the dimensions of the box that minimize the amount of material used to construct it.

Q: A box is to be constructed from a piece of square cardboard whose perimeter is 36 inches by cutting…

A: maximum volume

Q: A closed rectangular box of volume 324 cubic inches is to be made with a square base. If the…

A:

Q: With only 600 m2 of materials, a closed cylindrical tank is to be made. What should be the height of…

A: Let's find.

Q: A rectangular garden of area 480 square feet is to be surrounded on three sides by a brick wall…

A:

Q: Find the maximum and minimum volumes of a rectangular box whose surface area equals 8000 square cm…

A: Let the three sides or edges of the rectangular box be a,b and c in cm. Surface area of the box will…

Q: 2. A rectangular area is enclosed with fencing on three sides, with the fourth side along a house.…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: The school director of Saint Louis School of Pacdal, Inc, wants to construct a rectangulr wants to…

A: To find: The dimensions of the garden to be maximized: Given information: The school director wants…

Q: A piece of wire of length 60 is cut, and the resulting two pieces are formed to make a circle and…

A: Let x be the length of the wire cut for the circle then the length of the wire cut for the square.If…

Q: A jewelry box with a square base is to be built with copper-plated sides, nickel-plated bottom and…

A: Jewelry box having specification; square base, Let the side of square base = a cm.…

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: A courier service will deliver a package only if the length plus girth does not exceed 108 inches.…

A: Given: A courier service will deliver a package only if the length plus girth does not exceed 108…