Max Capacity Trapezoid Trough: Optimization Problem Q

In summary, the area of a trapezoid can be calculated using the formula A = ½(b1 + b2)*h, where b1 and b2 are the lengths of the parallel sides and h is the perpendicular distance between them. To maximize the area, a relation between h and the angles of the side planks should be found, and then A can be maximized with respect to these angles.
  • #1
griffon
3
0
Q: A trough is to be made from three planks, each 12 in. wide. If the cross section has the shape of a trapezoid, how far apart should the tops of the sides be placed to give the trough maximum carrying capacity?

OK the area of a trapezoid is
A=2bh
I know that much, but I've been struggling with this one, off and on, for about two days. I just don't know where to start. I'm not looking for an answer, just a starting point please. :confused:
 
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  • #2
The area of a trapezoid is,

A = ½(b1 + b2)*h

where b1 and b2 are the lengths of the parallel sides and h is the perpindicular distance between them.

You want to maximise this area, so find a relation between h and (b1 and b2) using the angle the side plank is at.

Then A is a function of the angle. Maximise A wrt the angle.
 

FAQ: Max Capacity Trapezoid Trough: Optimization Problem Q

What is a Max Capacity Trapezoid Trough?

A Max Capacity Trapezoid Trough is a type of container with a trapezoidal cross-section that is used to hold and transport large amounts of liquid or material. It is designed to maximize the amount of material that can be held within its dimensions.

How is the Max Capacity Trapezoid Trough used?

The Max Capacity Trapezoid Trough is commonly used in industrial and agricultural settings to transport and store liquids such as water, chemicals, and fertilizers. It can also be used to store and transport grains, sand, and other materials.

What is the optimization problem associated with the Max Capacity Trapezoid Trough?

The optimization problem with the Max Capacity Trapezoid Trough involves finding the dimensions that will maximize the volume of material that can be held within the trough while also accounting for factors such as stability, weight, and cost.

How is the optimization problem of the Max Capacity Trapezoid Trough solved?

The optimization problem of the Max Capacity Trapezoid Trough can be solved through mathematical calculations and modeling. This involves finding the optimal dimensions that will maximize the volume while also considering other factors such as material strength, weight distribution, and cost.

What are the benefits of using a Max Capacity Trapezoid Trough?

The main benefit of using a Max Capacity Trapezoid Trough is its ability to hold and transport large amounts of material efficiently. It also allows for more efficient use of space compared to other types of containers with a rectangular or cylindrical shape. Additionally, the trapezoidal shape of the trough allows for better weight distribution, making it more stable and easier to transport.

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