Find the Dimensions of a Rectangular Box

math hurts my head

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Jul 12, 2006
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I have two problems I would like some assitance on.

1) Find the dimensions of a rectangular box with a square base and no top that has volume 20,000 cubic centimeters and the smallest possible surface area.

2) a. A company makes novelty bookmarks that sell for $142 per hundred. The cost (in dollars) of making x hundred bookmarks is x^3 - 8^2 + 20x + 40. Because of other projects, a maximum of 600 books marks per day can be manufactured. Asumming that the company can sell all the bookmarks it makes, how many should it make each day to maximize profits?

b. Owing to a change in other orders, as many as 1600 bookmarks can now be manufactured each day. How many should be made to maximize profits.

I appreciate any help!
 
1) Pick a variable for the length of a side of the base. What then will be the area of the base?

You are given the volume. Use this value, along with the formula for the volume of a rectangular prism, to find an expression for the height in terms of the variable you picked for the length and width.

Now write expressions, using the variable and the height-expression, for the areas of the various faces of the box. Add to get an expression for the total surface area.

How do you find the max/min value of a quadratic?

2-a) Profit is revenue less costs. Use this fact to find the profit formula. Then find the maximizing value.

2-b) This works just like (2-a), except that you can look at the values of x between 0 and 16, instead of just 0 and 6.

If you get stuck, please reply showing what you have tried. Thank you.

Eliz.
 
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