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A closed box with a square base is to have a volume of 16000 cubic centimeters. The material
for the top and bottom of the box costs $3 per square centimeter while the material for the sides
costs $1.50 per square centimeter. Find the dimensions of the box that will minimize the total
cost of materials. What is the minimum total cost?

Respuesta :

michell96

The most suitable measurements for a box with a square base are 5cm (width) x 5cm (length) x 640cm (height). This box would be worth $4875

How to calculate the minimum value of the box?

To find the minimum value of a box that must have a square base and 16000 cm³, we must try different measurements to find the variable that represents the least value.

In this case, the variable that represents less value is a base of 5cm x 5cm and a height of 640cm. This means that the box would be worth $4875 as shown below.

Base

  • 5cm × 5cm = 25cm²
  • 25cm² x 3 = $75

Sides

  • 5cm × 640cm = 3200cm²
  • 3200cm² × $1.50 = $4800

  • $4,800 + $75 = $4,875

Additionally, we can check that the volume of the box is the required 16000cm³, as shown below:

  • 5cm × 5cm × 640cm = 16000cm³

Learn more about cubic centimeters in: https://brainly.com/question/9740005

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