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Modeling Your company is going to make its own boxes!
It has been decided the box should hold 0.45m3 (0.45 cubic meters which are equal to 45 liters) of nuts

and bolts.

The box should have a square base, and double thickness bottom.

Cardboard costs $0.47 per square meter.

It is up to you to decide the most economical shape and size. (Except that the base must be square.)

You must show how you have developed a model to decide the most economical size. In this assignment, it is suggested that you follow the following steps

(a)  Draw a sketch of your box and a sketch of a net from which your box can be constructed.

(b)  Make a formula for the volume and surface area of your box

(c)  Develop a formula for the cost of the box using the area and volume

(d)  Draw a graph of the cost of the box using the y-axis as the cost and x-axis as the width of the base.

Remember to include enough information to show us how you drew your graph. Include either the points you plotted or the formula and drawing package used if you found the graph electronically.

(e)  Use the graph to determine the minimum cost, width, and height of the box

(f)  What are your recommendations for the shape and dimensions of the box?