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17 Apr 2018

2. Suppose a rectangular box is to contain 10 cubic feet. The length of the box is to be twice the width. Material for the box costs $2 per square foot for the bottom of the box, $1 per square foot for the sides of the box and $3 per square foot for the top of the box. Find the dimensions of the box that would minimize the cost.

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Nestor Rutherford
Nestor RutherfordLv2
17 Apr 2018
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Related questions

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?

[12] 4. A rectangular storage container with an open top is to have volume of 8 cubic metres. The length of its base is twice the width. Material for the base costs $4.50 per square metre, and material for the sides costs $6 per square metre. Find the cost of the material for the cheapest such container. Answer:

9. A box with a square base and open top must have a volume of 4000 cm3. Find the length of the base that should be used to minimize the amount of material used.

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