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Optimize Box Volume & Find Minimum Sums
- 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.