CEE 3000 HW 3 Solutions Fall 21

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School

Georgia Institute Of Technology *

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Course

3000

Subject

Civil Engineering

Date

Oct 30, 2023

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pdf

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Uploaded by catelynchamblee

Georgia Institute of Technology | School of Civil & Environmental Engineering CEE 3000: CIVIL ENGINEERING SYSTEMS HOMEWORK 3: MATH TOOLS Fall 2021 Assigned:9/21/2021 | Due: 10/05/2021 Name: _____________________________________ Date: __________________________________ 1. Assume that you’ve been hired by a contractor specializing in the supply of storage sheds. Your employer has just obtained a contract from a Department of Transportation (DOT) in a northern state to manufacture sheds to hold sand or salts. These will used to keep their highways open to traffic in periods of heavy snow. The consultant will use a durable material recently developed to have an average useful life almost 15% longer than the average useful life of competing materials on the market, when properly maintained. Each shed must hold a volume of 14,500 m 3 . The rectangular base pad costs $75/m 2 , the materials on the sides and roof cost $45/m 2 and $50/m 2 , respectively. These special sheds are cuboid in shape. For stability, the DOT requires the width of the base to be half the height of the shed. The DOT desires the optimum design that results in the least total cost of materials. Your first task is to determine the optimum design dimensions for the sheds. Answer the following questions. (10 points) (a) What design dimensions will minimize the total material costs? (5 points)

2 Width = 18.31 meters Length = 21.63 meters Height = 36.62 meters (b) What is the optimum cost of each shed (to the nearest 100 thousand)? (3 points) Optimum cost = $200,000 (c) After doing some quick research to cross check the cost estimates you were given, you have just found out that the materials may cost up to 10% more than the original estimates given. The DOT would like to purchase 5 sheds. How much money should they budget for the sheds (in millions)? (2 points)

3 Budget: $0.995 million ~$995,000

4 2. For the construction of a civil engineering facility, a contractor has found natural reserves of sand and gravel at Beaver Plains and Valley View for sale. The unit cost of material including delivery is $6 and $8 from Beaver Plains and Valley View, respectively. After the material is brought to the site, it is mixed thoroughly and uniformly. The contract specifications state that the mix should contain a minimum of 30% sand. A total volume of 100,000 m 3 of mixed material is needed for the project. The Beaver Plains Pit contains 25% sand and the Valley View Pit contains 50% sand. As the new construction engineer on the project, you have been asked to determine how much material should be taken from each pit in order to minimize the cost of the material. Answer the following questions. (10 points) (a) What are the decision variables? (1 point) X = Amount from Beaver Plains Y = Amount from Valley View (0.5pts each) (b) Write the constraints in mathematical form? (2 points) (0.5pts each) (c) How much material should the contractor take from each pit in order to minimize the overall cost of the material? Find the optimum solution. (6 points)

CEE 3000 HW 3 Solutions Fall 21

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