Pipeline for Math Calculus 1

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In this guide you will find a well thought out plan to construct a pipeline which will run through a wetland. The concept of the derivative will be used to regulate the minimum cost for this construction plan.

Figure 1 displays the ideal construction of the pipeline, if done correctly. The pipeline should start at point A and run directly along the swamp for approximately 674.5 ft. and cut through the swamp for about 305.4 ft. to point B. Attached to the proposal are the computations of what led to the cost function and the final cost. Using figure 2, calculations were performed to achieve this.

First the cost was estimated using the formula:



The derivative was then taken from Cost(x) to evaluate the cost at its minimum and the cost function was created.


Once the cost function was established, it was simplified and set to 0 to solve for x. This gave the distance in dry land and the distance in wetland in feet. These calculations are also shown in the attached computations. x had two answers, 674.54 and 1025.55. These were the critical points; 674.54 being the minimum feet and 102.55 being the maximum feet. Considering the pipeline construction needs to be done at a minimum cost, the minimum ft. was used for x. W was also found in terms of x. 674.54 feet was plugged in for the x- value and the total minimum cost was achieved. According to the calculations, the total minimum cost is $3256.78.

Following this guide will be crucial in constructing the pipeline correctly and efficiently. If all calculations are shadowed the total minimum cost should come out to $3256.78.

Katryna Cruz...
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