Question

A container manufacturer plans to make rectangular boxes whose bottom and top measure x by 4x. The container must contain 8cm3. The top and the bottom will cost $3.90 per square centimeter, while the four sides will cost $4.90 per square centimeter.
What should the height of the container be so as to minimize cost? Round your answer to the nearest hundredth.

Answer 1

The most efficient measurements of the box should be 4cm long, 1cm wide and 2cm high so that its cost is $129.2

How to calculate the measures of the rectangular box?

To calculate the measurements of the rectangular box we must take into account the following condition:

• Bottom and top measure x by 4x.

According to the above, we can establish that the most appropriate measurement for the bottom and top should be 1cm (width) × 4cm (length). Additionally we can establish that the height of the box would be 2cm.

How to find the volume of this box?

To find the volume of the box we must use the following formula:

• height × width × length = volume.
• 2cm × 1cm × 4cm = 8cm³

What are the areas of this box?

The areas of this box are:

• Bottom and top: 1cm × 4cm = 4cm²
• Sides: 1cm × 2cm = 2cm²
• Front and rear: 2cm × 4cm² = 8cm²

What is the price of this box?

The total price of this box is as follows:

Top and bottom:

• 4cm² × $3.90 = $15.6
• $15.6 × 2 = $31.2

Sides:

• 2cm² × $4.90 = $9.80
• $9.80 × 2 = $19.6

• 8cm² × $4.90 = $39.2
• $39.2 × 2 = $78.4

• $78.4 + $19.6 + $31.2 = $129.2

Learn more about boxes in: brainly.com/question/23952628

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