1. For this project, we locate a trash dumpster in order to study its shape and construction. We then attempt to determine the dimensions of a container of similar design that minimize the construction cost.

a. 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.

b. While maintaining the general shape and method of construction, determine the dimension 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 of 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 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.

c. Describe how any of your assumptions or simplifications may affect the final result.

d. If you were hired as a consultant on this investigation, what would your conclusions be? Would you recommend altering the design of the dumpster? If so, describe the savings that would result.

Please help me solve this question using Linearization with two variables.