Question

A container manufacturer plans to make rectangular boxes whose bottom and top measure 2x by 3x. The container must contain 12in.3 The top and the bottom will cost $2.60 per square inch, while the four sides will cost $4.30 per square inch. What should the height of the container be so as to minimize cost? Round your answer to the nearest hundredth.

Answer 1

The height of the container be so as to minimize cost will be 1.20. inches.

How to calculate the height?

The volume of the box will be:

= 2x × 3x × h

= 6x²h

Volume = 6x²h

12 = 6x²h

h = 2x²

The cost function will be:

C = 2.60(2)(6x²) + 4.30(12x)h

C = 31.2x² + 51.6xh

Taking the derivative

62.4x + 51.6h

h = 1.20

Therefore, the height of the container be so as to minimize cost will be 1.20 inches.

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