数学建模

The Managing Water Storage Problem

Background Information:

Current research in the engine horsepower-to-weight ratio focuses on decreasing the weight of an engine while still increasing the horsepower output. A significant drawback, up until now, was the lack of a high grade metallic alloy that could reduce the engine weight, but still show an increase in the

horsepower-to-weight ratio. Such a discovery of this metallic alloy was found in abundance in a small third world country called Igotit. Political negotiations between the United States and Igotit went extremely well and we obtained exclusive rights to mine the alloy. Without going into the details of the agreement, the United States must upgrade existing lines of communication near the small town of Igotitville, capital of Igotit, which are in a severe state of decay. The political agreement specifically requires us to:

1. Construct a water storage reservoir dam,

2. Design and construct a city water storage tank,

3. Improve the existing traffic control system.

These tasks must be initiated before we can consider mining operations. Finally, construction units must start arriving within six months to begin the work, and at least 50% of the required work must be done before we can begin mining

operations. The 62d Engineer Battalion (CBT HVY) will spearhead the move to Igotitville and retain the overall responsibility for the completion of all horizontal and vertical construction tasks outlined in the political agreement between the two countries. The battalion (BN) Operations Officer (S3) identified mission essential tasks that need to be completed before the battalion deploys. After tasking your company for support, the company commander gives you the responsibility to report to the BN S3 for mission details. Upon reporting, the BN S3 promptly outlines the following three missions you must complete.

Problem:

MISSION #1: Determine the time, in work days, to construct a water reservoir dam according to the design specifications below. Assume the battalion will divert five each Caterpillar 622B earthmovers to support this mission and that we will work ten hour workdays. Each earthmover is capable of moving 6 cubic yards of soil to the dam site every one-half hour. Determine the rate of change in the height of the dam when it is two-thirds of the planned height. Does this rate increase or decrease as the dam is constructed?

MISSION #2: Design and minimize the material needed to construct a 32500 (g) gallon water storage tank that will provide emergency water supplies and line pressure for the city of Igotitville's drinking water system. The basic design is to utilize a tank with a spherical bottom, a r cylindrical center, and a conical cap. The sketch of the water tank is given to the right. The height of the cap must be 0.10 (p) of the radius. The material costs about 3.00 (m) dollars per square foot, but comes in sheets that that measure 0.5 inches thick by four feet wide by eight feet r long.

MISSION #3: Prepare a complete bill of materials (BOM) for the construction of six traffic lights that will minimize the construction cost. Traffic light poles are 30 feet long and buried eight feet in the ground. The traffic light can hang no lower than 16 feet off the ground. The tension of the cable is the chief factor in the cost of the traffic light system. The uniform radius between the poles and traffic light is 85 (r) feet and each traffic light weighs 22 (w) pounds.