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nekit [7.7K]
3 years ago
6

Please answer it’s due!!

Mathematics
1 answer:
Nitella [24]3 years ago
4 0

Answer:

42

Step-by-step explanation:

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Suppose that you are to make a rectangular box with a square base from two different materials. The material for the top and fou
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height = 14.5 ft

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Step-by-step explanation:

Let the side of the square base is a and the height of the box is h.

The material required to make the box is equal to the total surface area of the box.

Area of base = a²

Cost of square base is $ 2 per ft²

So, the cost of making base = 2a²

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Total cost of making the box = 2a² + 3a² + 2ah = 5a² + 2ah

According to the question

144 = 5a² + 2ah

h = \frac{144-5a^{2}}{2a}     .... (1)

The volume of the box is V = length x width x height

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V = 72 a - 2.5 a³     from equation (1)

Differentiate both sides with respect to a.

dV/da = 72 - 7.5 a²

Put, it equal to zero for maxima and minima

7.5 a² = 72

a = 3.2 ft

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h = \frac{144-5\times 3.2\times 3.2}{2\times 3.2}

h = 14.5 ft

So, the dimensions of the box are

height = 14.5 ft

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