1. Oscar the Grouch

2. Clearly (re)state the problem to be solved?  The problem we were trying to solve was to create a dumpster for Oscar the Grouch and to keep costs at a minimum. The dumpster needed to have the same volume as the dumpster we measured, which was 71.35 cubic feet.

3. Provide a explanation to how the problem will be approached?  To solve the problem, we measured an actual dumpster and calculated the volume. We then created a Maple worksheet showing how this constrained optimization problem would be solved.  TC in terms of L, W, and H =.7×{2(L×H)+2(W×H)} +.9×{L×W} +.18×{2L+2W+4H}  Volume (Constraint equation) = 71.35 = L×W×H  L=x, W=y, H=z

4. State the answer in a few complete sentences which stand on their own?  After trying different values in maple, We found that a length of 4.84 feet, a width of 4.84 feet, and a height of 3.04 feet would create a dumpster of the same volume with the minimum total cost.

5. Give a precise and well-organized explanation of how the answer was found?  We measured the lengths of a dumpster at SCC’s parking lot and then we used several calculations in maple to find the final answer.

6. Clearly label diagrams, tables, graphs, or other visual representations of the math?  All the math we used in this project is represented by the following Maple file:

7. Define all variable, terminology, and notation used?  X=Length  Y=Width  Z=Height  The decimal numbers used in the TC formula represented the costs per square foot of the sides, base, welding, etc.  The decimal numbers used in the TC formula represented the costs per square foot of the sides, base, welding, etc.

8. Clearly state the assumptions which underlie the formulas and theorems, and explain how each formula or theorem is derived, or where it can be found? Clearly state the assumptions which underlie the formulas and theorems, and explain how each formula or theorem is derived, or where it can be found?  We used the method of Lagrange Multipliers which provides a strategy for finding the maximum/minimum of a function subject to constraints.  The method of Lagrange Multipliers is explained in details at Mr. Clark’s website section 15.3.

9. Give acknowledgment where it is due?  The only source we used for help was Mr. Clark’s website: http://www3.sc.maricopa.edu/clark/

10. Does this presentation contain correct mathematics and solves the problem that was asked?  Yes we believe that the mathematics were correct and it solves the problem that was asked.