optimization] ‘a square box with a base and open top must have a volume of 62,500 cm^3. Find the dimensions of the box (base and height) to minimize the amount of materials used.’ —I don’t know what the objective function would be.
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A: We will find the dimensions of the box.
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A:
Q: A rectangular bird sanctuary is being created with one side along a straight riverbank. The…
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Q: A rectangular garden of area 320 square feet is to be surrounded on three sides by a brick wall…
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Q: A rectangular box is going to be made with a volume of 274 cm3 . The base of the box will be a…
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Q: A rectangular bird sanctuary is being created with one side along a straight riverbank. The…
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Topic = Functions
Step by step
Solved in 2 steps
- What size square should be cut out of the index card in order to maximize the volume of the box?a cylindrical container that has a capacity of 4000 cubic centimeters is to be produced. The top and bottom of the container are to be made of material that costs $0.50 per square centimeter, while the sides of the container are to be made of material costing $0.40 per square centimeter. Find the dimensions that will minimize the total cost of the container.A rectangular garden of area 480 square feet is to be surrounded on three sides by a brick wall costing $12 per foot and on one side by a fence costing $8 per foot. Find the dimensions of the garden such that the cost of the materials is minimized.
- A box with an open top and a square base must have a volume of 32 cubic meters. How do you find the dimensions of the box that minimize the amount of material used?A farmer wants to fence an area of 37.5 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. What should the lengths of the sides of the rectangular field be so as to minimize the cost of the fence? smaller value: larger value:A rectangular portion of a pasture next to an irrigation canal is to be enclosed by a fence with no fence being required along the canal. If the area of the rectangular pasture is to be 87362 square feet, what dimensions will be required to minimize the amount of fence?
- A box is to be constructed from a piece of square cardboard whose perimeter is 36 inches by cutting equal squares out of the corners and then turning up the sides. Find the maximum volume of the box that can be made this way.An open box is formed by cutting identical squares from each corner of a 10 inches by 10 inches sheet of paper. Find the dimensions of the box that will yield the maximum volumeA rectangular area of 5000 sq st is to be enclosed by a river on one side. Find the dimensions of the fence that will minimize the fencing materials used. Verify that what you find will result in minimum fencing used.
- A storage box with a square base must have a volume of 80 cubic centimeters. The topand bottom cost $0.20 per square centimeter and the sides cost $0.10 per square centimeter.Find the dimensions that will minimize cost.A farmer wants to fence an area of 13.5 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. What should the lengths of the sides of the rectangular field be so as to minimize the cost of the fence?A residential area will be built with a rectangular green space of two square meters, with paved walkways around the green room. The long-sided sidewalks of the green space are required to be three meters wide and the short side of the sidewalks four meters wide. How do we design the length and width of the green room to minimize the footprint of the paved walkways?
