A storage box with a square base must have a volume of 90 cubic centimeters. The top and bottom cost $0.40 per square centimeter and the sides cost $0.20 per square centimeter. Find the dimensions that will minimize cost. (Let x represent the length of the sides of the square base and let y represent the height. Round your answers to two decimal places.) x = y =

Q: A manufacturer of open steel boxes has to make one with a square base and a volume of 1 m3. The…

A: Given that ,Volume of open steel box = 1m3    volume of box = x.x.ysteel cost $2 per square unit(a)…

Q: A container manufacturer plans to make rectangular boxes whose bottom and top measure x by 3x. The…

A: Let h be the height of the rectangular box. Here, the objective is find the value of h to minimize…

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

A: Solution : We given the volume of the box v = 50 ft2 Cost of material used to build top and bottom…

Q: The base of a rectangular prism shaped aquarium without a lid is made of slate and the sides are…

A: Given Volume of the tank V=96 m3 Cost of slate (S) = 3 Cost of Glass (G) (per unit area) S=3G

Q: Luke needs to build a shed to store his family's moisture vaporators. The shed must have a volume of…

A: The shed must have a volume of 202,500ft3 and must be in the shape of a rectangular box whose base…

Q: Please

A:

Q: A worker is to construct an open rectangular box with a square base and a volume of 27 ft°. If…

A:

Q: A natural gas company is laying an underground natural gas pipeline in a new subdivision on both…

A: Solution: Let cost for laying underground = P      cost for laying underwater = 2P

Q: Luke `needs to build a shed to store his family's moisture vaporators. The shed must have a volume…

A:

Q: Give the cost function C=10x + 1,000/x , find the number of unit x to get the minimum cost.

A: The given cost function is

Q: An open box with a square base is to have a volume of 1500 cm³. What should the dimensions of the…

A: The volume of a box with a square base x by x cm and height h cm is V = x2h  The amount of material…

Q: A worker is to construct an open rectangular box with a square base and a volume of 98 ft°. If…

A:

Q: A rectangular box is to have a square base and a volume of 63 ft3. If the material for the base…

A:

Q: A Norman Window has the shape of a rectangle surmounted by a semicircle. If a Norman window is to…

A: Given, The perimeter of the window = 28 ft  Height of rectangular part = y width of rectangular part…

Q: A pencil cup with a capacity of 80 in^3 is to be constructed in the shape of a rectangular Box with…

A:

Q: A cylindrical can is to be made using a metal sheet. If the volume of the cylinder is 432π in3, then…

A: To find: The radius to minimize the material to be used: Given: The volume of cylinder is 432π cubic…

Q: Find a formula C(x,y,z) that gives the cost materials for the closed rectangular box, with…

A:

Q: A box with a square base and open top must have a volume of 32,000cm^3. Find the dimensions of the…

A: Given Data: The volume of the box is: V=32000 cm3 Let, The side of the square base is x and the…

Q: Lone Depot and Homes are two competing home improvement stores. Each claims to provide customers…

A: Notice that the container has square base with length x ft. The height of the container is y ft. The…

Q: In constructing an open rectangular box from 75 ft² of material, what dimensions will result in a…

A:

Q: Given a closed box with surface area = 16 and a square bottom, what value of x will maximize the…

A:

Q: A cylindrical can Is to have volume 1600 cubic centimeters. Determine the radlus and the helght…

A:

Q: A small shed is to be built with a volume of 125 ft3 and the cost is to be minimized. The concrete…

A: Let the length of the shed be l ft, width be b ft and height be h ft.Use the volume to find h in…

Q: A rectangular box with a square base and an open top must have a volume of 864 cm'. The box should…

A: Let the length and width of the box be: x Let the height of the box be: h Volume of the box is: 864…

Q: The volume of a rectangular box with length x, width y and height h is given by V=hxy. If the…

A:

Q: A company needs to manufacture cylindrical cans out of tin, each of which must have both a bottom…

A:

Q: A rectangular box with a volume of 980 ft is to be constructed with a square base and top. The cost…

A: Given information: The volume of the rectangular box is 980ft3. The rectangular box is square from…

Q: A truncated prism has a rectangular base whose length is twice its width. The corner heights are 16…

A: Find your answer below

Q: A worker is to construct an open rectangular box with a square base and a volume of 8 ft°. If…

A: Let the height of the rectangular box be h. As the base of this box is a square, let the sides of…

Q: A company needs to manufacture cylindrical cans out of tin, each of which must have both a bottom…

A: Here we solve the given problem of calculus.

Q: D If C) = 16,000 +2001 +*4x5 in dollars, find ) the cost, avera qe cat , and marg inal cost at a…

A: The change in the total cost, when an additional unit of the product is sold is called the marginal…

Q: .A rectangular storage with a square base has a volume of 100 in³. The top and bottom materials cost…

A: Given: A rectangular storage with square base has volume =100in3 top and bottom  material cost $4…

Q: A box with a square base and open top must have a volume of 100 cm3 . The material for the bottom…

A:

Q: A rectangular storage container without a lid is to have a volume of 10 m. The length of its base is…

A: Given data:     The given area of the rectangular field is: A=13.5 million square feet. The given…

Q: A rectangular corral of 96 square meters is to be fenced off and then divided by a fence into two…

A: We use second derivative test to find dimensions where amount of fencing is minimum

Q: The base of an aquarium (in the shape of a cuboid) with given volume V is made of slate and the…

A:

Q: Lone Depot and Homes are two competing home improvement stores. Each claims to provide customers…

A: Notice that the container is having square base with the length x ft . The height of the container…

Q: A worker is to construct an open rectangular box with a square base and a volume of 147 ft3. If…

A: Consider the given information about the box:

Q: The cost of producing an ordinary cylindrical tin can is determined by the materials used for the…

A: Given:       Volume =1000 cm3       Volume of cylindrical tin V=πr2h      then,            πr2h=1000…

Q: A closed rectangular container with a square base is to have a volume of 2592 in. The material for…

A: Given: A closed rectangular container with a square base is to have a volume of 2592 in3. The…

Q: A manufacturer of open steel boxes has to make one with a square base and a volume of 1 m3. The…

A:

Q: A tank with rectangular base and sides and open at the top, is to be constructed so that its depth…

A:

Q: A rectangular box with no top is to be constructed having a 125 cubic inches. What width r, in 2…

A:

Q: The base of a rectangular prism shaped aquarium without a lid is made of slate and the sides are…

A: Given V=96 m3 Let the dimension is x, y and z Hence, Volume is given by V=xyz......1 The equation…

Q: N-N-OUT manufacturer of food-storage containers makes cylindrical can with a volume of 500…

A:

Q: A poster is to contain 300 m^2 of printed matter with margins of 10 cm at the top and 5 cm at each…

A:

Q: A company that produces cell phones has a cost function of C = 12x2 – 89x + 16981, where C the cost…

A:

Q: Find the dimensions of a open topped box that maximizes the volume with the constraint that the…

A: We will use Lagranges multiplier method to find dimension of the box .