I've been stuck on this question for more than an hour and I still can't seem to get the right answer (). So here goes:(adsbygoogle = window.adsbygoogle || []).push({});

Question:Sindy is building a rectangular wooden btoy chest so that its length is two times its width. She has picked pine for the top, front, and two sides of the chest. She will use fibreboard for the back and bottom. The chest much have volume of 0.3m^3. Pine costs twice as much as fibreboard. Find the dimensions that will minimize the cost of the chest.

My wrong calculations:

Let a be the price of fibreboard, and 2a be price of pine.

2x^2y = 0.3

so 7 = 0.3/(2x^2)

Cost = 2a (2xy + 2x^2 + 2xy) + a (2xy+2x^2)

= 10axy + 6ax^2

= 10ax(0.3/2x^2) + 6ax^2

= (1.5a/x) + 6ax^2

Now if I take the derivative of this, I get:

Cost' = -1.5x^(-2) + 12x

1.5 = 12x^3

0.125 = x^3

x = 0.5

And so, y=0.6

The correct answer shold be 0.585m x 1.170m x 0.438m, so any help would be great as to what I'm doing wrong!

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# Homework Help: Pine costs twice as much as fibreboard

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