1. First locate a trash Dumpster in your area. Carefully study and describe all
ID: 2862290 • Letter: 1
Question
1. First locate a trash Dumpster in your area. Carefully study and describe all details of its construction, and determine its volume. Include a sketch of the container. 2. While maintaining the general shape and method of construction, determine the dimensions such a container of the same volume should have in order to minimize the cost of construction. Use the following assumptions in your analysis: The sides, back, and front are to be made from 12-gauge (0.1046 inch thick) steel sheets, which cost $0.70 per square foot (including any required cuts or bends). The base is to be made from a 10-gauge (0.1345 inch thick) steel sheet, which costs $0.90 per square foot. Lids cost approximately $50.00 each, regardless of dimensions. Welding costs approximately $0.18 per foot for material and labor combined. Give justification of any further assumptions or simplifications made of the details of construction. 3. Describe how any of your assumptions or simplifications may affect the final result. 4. If you were hired as a consultant on this investigation, what would your con- clusions be? Would you recommend altering the design of the Dumpster? If so, describe the savings that would result 308=volume=lxw+{.5(h-x)l}w... use this to eliminate a variable l=308/(.5hw+.5xw) cost=c=.7(sides+back+front)+90+.9base+welding(.18) sides={xl+.5(h-x)l}2=2xl+hl-xl=xl+hl back=hw front=xw base=lw welding =2h+2l+2x+2w cost=c=.7(xl+lh+hw+xw)+90+.9lw+.18(2h+2l+2x+2w)
Explanation / Answer
According to condition
Based on your findings, with l,b,h feet being dimensions of the dumpster, find an expression for construction cost. If I interpret your information correctly, it should be
0.7×2(l+b)h+0.9lb+50+0.18(lb+2(l+b)h
=50+1.76bh+1.08bl+1.76hl
So for a given fixed volume V=lbh
Here we want to minimise 1.76bh+1.08bl+1.76hl
so the sum gets minimised when all terms are equal. This gives us
1.76bh=1.08bl=1.76hl
1.76/l=1.08/h=1.76/b
so l=b=1.761.08h
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