Optimization 1.3.08
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The document discusses optimizing the dimensions of boxes with given surface areas to find the maximum possible volume. It provides problems to find the minimum sum of two numbers whose product is given. Specifically, it asks to find the dimensions of a box with a square base and 108 in^2 surface area that gives the maximum volume. It also asks to find the minimum sum of two numbers whose product is 100, 200, and where the product is 50 and the sum of the first plus twice the second is minimum.
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Optimization 1.3.08
- 1. We could all use a little Optimization
- 2. If we are going to design a box with a square base and a surface area of 108 in 2 , what is the maximum volume of the box and what dimensions give that Volume? I. Write V in terms of x alone. II. Determine the Domain of V(x).
- 3. III. Find the Critical Points of V(x) . IV. Find the maximum Volume and the Dimensions.
- 4. Find two numbers whose product is 100 and whose sum is minimum.
- 5. Find two numbers whose product is 200 and whose sum is minimum. Find two numbers whose product is 50 and the sum of the first plus twice the second is a minimum.