A common problem encountered by the oil industry is to determine the most cost-effective route to connect various wells in an oil fertile area. The attached map is a copy of a section of a U.S. Geographical Survey contour map with a wetland area outlined. An existing oil well is located approximately at the point labeled A. A new well is to be dug at point B, requiring that the pipeline installation company be given plans for laying connecting pipe from A to B. In consultation with the installation company, the following information has been obtained:
• Straight, two-inch coated pipe must be used, at a cost of $ 1.50 per foot.
• A maximum of one elbow joint may be used. The elbow joint may be fabricated with any angle measure and will not be included in the cost.
• On normal terrain, installation cost is $ 1.20 per foot.
• Installation in the wetland area requires the use of a special , at an additional installation cost of $ 60 per hour over and above normal installation cost.
• In a 10-hour day, this special can dig approximately 300 feet of trench.
Write up your investigation as a report to your supervisor, who should be able to understand your report without reference to this sheet. Demonstrate that you and your partner(s) have considered the costs of what you believe to be several viable pipeline routes connecting the existing well at A to the new well at B. Discuss your selection for the route that incurs the least cost and mathematically justify that your selection will give the least cost of all possible routes from A to B. Be sure to explain why minimum distance may not yield minimum cost.
Hints:
• Since the wetland separating A and B is very irregular in shape, simplify your work from the beginning by making some (slightly exaggerated) assumptions. You are to assume that the entire wetland is in the shape of a rectangle. How far to the east will your rectangle go? How far to the west? To the north? To the south?
• Reduce the number of paths you consider before calculating anything. Should you consider a path around the swamp to the north of A (with only one elbow joint)? What about to the south of B? Can you really go due south of A only on normal terrain?
• Do some measuring and calculating of costs of various paths, but be sure you consider the case where the pipeline is laid some distance southeast of A on wetland terrain and then turns due south on normal terrain to B. Perhaps this is where calculus comes in?
ms sue please help me.
If you type in this :Engineering Applications in Differential and Integral Calculus* onto google on page four you will see the map. Please help
the title of this lab is designing a pipeline with minimum cost
Title: Oil Industry Pipeline Route Analysis Report
Introduction:
In this report, we will explore several viable pipeline routes connecting an existing oil well at point A to a new well at point B. Our objective is to determine the route that incurs the least cost. We will consider the costs of pipe materials, installation, and take into account the irregular wetland area between points A and B.
Simplifying Assumptions:
To simplify our analysis, we will assume that the entire wetland area between points A and B can be approximated as a rectangular shape. In reality, this may not be the case, but for the purpose of this investigation, it will allow us to make calculations and comparisons.
Determining the Dimensions:
Based on the provided map, we need to determine the extent of the wetland area. We can measure the approximate distance to the east, west, north, and south of point A and point B. These measurements will help us define the dimensions of our rectangular approximation.
Reducing the Number of Paths:
To streamline our analysis, we can eliminate certain paths. For example, considering a path around the swamp to the north of point A with only one elbow joint might not be the most cost-effective option. Similarly, going directly south of point A on normal terrain may not be feasible due to potential obstacles.
Calculating Costs:
We need to calculate the costs associated with various pipeline routes. The factors that contribute to the costs include pipe materials and installation.
1. Pipe Materials:
We are given that two-inch coated pipe must be used, which costs $1.50 per foot. The total cost of pipe materials for a specific route can be calculated by multiplying the length of the pipe required for that route by the cost per foot.
2. Installation:
a) Normal Terrain: The installation cost on normal terrain is $1.20 per foot.
b) Wetland Terrain: Installation in the wetland area requires a special , with an additional cost of $60 per hour (over and above normal installation cost). The special can dig approximately 300 feet of trench in a 10-hour day.
Evaluating the Routes:
We should consider various routes from point A to point B and calculate the associated costs for each route.
Mathematical Justification:
To determine the route that incurs the least cost, we need to consider both the pipe materials cost and the installation cost. Simply choosing the minimum distance between points A and B may not yield the minimum cost. This is because the additional costs associated with the wetland terrain must be taken into account.
Conclusion:
Based on our investigation, we can identify the pipeline route that incurs the least cost from point A to point B. By comparing the costs of different routes and considering the specific conditions of the wetland terrain, we can mathematically justify that our selection provides the least cost among all possible routes.
Further analysis, calculations, and comparisons can be conducted to validate and refine the selected route, taking into account additional factors such as potential obstacles, environmental considerations, and safety requirements.