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The model is not the same as the real thing. In our example we did not think about the thickness of the cardboard, or many other "real world" things. But hopefully it is good enough to be useful.

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Example: An ice cream company keeps track of how many ice creams get sold on different days. They can then predict future sales based on the weather modell, and decide how many ice creams they need to make The model is not the same as the real thing. Still not perfect did we consider wasted space because we could not pack things neatly, etc But there are still "real world" things to think about, such as "will it be strong enough?

The box shape could be cut out like this but is probably more complicated : Step Two: Make Formulas.

How lookint we write this as an equation? At first glance there is nothing to model, because there was no change in production. Well, the formula only makes sense for widths greater than zero, and I also found that for widths above 0.

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Step One: Draw a sketch! So a model is not reality, but should be good enough to be useful. But hopefully it is good enough to be useful.

Is this box a good shape for packing, handling and storing? But maybe we need more accuracy, we might need to send hundreds of boxes every day, and the thickness of the cardboard matters. Your company is going to make its own boxes!

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They recently had their break modfl reduced by 10 minutes but total production did not improve. But wait a minute Playing With The Model Now we have a model, we can use it in different ways: Example: Your company uses xx mm size boxes, and the cardboard is 5mm thick. It can also be useful when deciding which box to buy when we need to pack things. Example: on our street there are twice as many dogs as llooking.

Computer Modeling Mathematical models can get very complex, and so the mathematical rules are often written into computer programs, lkoking make a computer model. It helps to sketch out what we are trying to solve! Any other ideas you may have! Someone suggests using 4mm cardboard By comparing this to the weather on each day they can make a mathematical model of sales versus weather.

The box should have a square base, and double thickness top and bottom. Predicting the Future Mathematical models can also be used to forecast future behavior.

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It is up to you to decide the most economical size. In our example we did not think about the thickness of the cardboard, or many other "real world" things. ffun

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In other words: when the width is about 0. In fact, looking at the graph, the width could be anywhere between 0. So let's see if we can improve the model: The cardboard is "t" thick, and all measurements are outside the box The base mocel square, so we will just use "w" for both lengths The box has 4 sides, and double tops and bottoms.

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You could recommend: looking at production rates for every hour of the shift trying different dun times to see how they affect production A Bigger Example: Most Economical Size OK, let us have a go at building and using a mathematical model to solve a real world question. So the model is useful! It has been decided the box should hold 0.

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If we are charged by the volume of the box we send, we can take a few measurements and know how much to pay. That could be hard to work with So here is lpoking plot of that cost formula for widths between 0. But we can make it simpler!

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