Problem on Lab Assessment: A company wants to lay pipeline from point A (a drilling rig) to point B (a refinery) which will require going under a river. They would like to minimize the total cost of laying the pipeline. The width of the river is 12 miles, and the horizontal distance from the Rig to the Refinery is 20 miles: A (Drilling Rig) pipeline underwater pipeline underground B (Refinery) 20 miles a) If the cost to lay pipeline underground is $30,000/mi and the cost to lay pipeline under water is $50,000/mi, determine a function that gives cost as a function of x (where x is the distance from point D to point P). In other words, find a function, C(x), so that if I plug x into your function I get out the total cost of laying the pipe from point A to point P to point B. (Hint: This is not much different than the ramp situation in warm-up problem b) Now, say I let x-6 in your equation from part a, I would get the cost if I located the point P six miles down the "coast" from point D. That would make the length of the pipeline underground 14 miles and it would make the length of the pipeline underwater about 13.4 miles which you can get from the Pythagorean Theorem. Question 1: Evaluate C(O and then interpret the result; that is, what is the total cost and what path is taken to obtain this cost? Question 2: Repeat for C(20) c) Find the minimum total cost to lay the pipeline and how we should lay it. There are three different ways in which I would like you to do this i. Graphically. Use your calculator to graph the cost function in a viewing rectangle that clearly shows the location of the minimum cost. tar mingh. ii. Numerically. Evaluate C(x) for many (not too many) values between 0 and 20 inclusive. Then look at the results and from them determine the minimum cost Question 4: Fill in the table in the assessment. Question 5: Use the information in the table to determine the minimum cost. iii. Analytically. In other words, use the first derivative of C(x) the way I did in warm-up problem 2. Feel free to use http://www.wolframalpha.com/, but be sure to verify that you actually have a minimum Question 6: State the equation you solve to get the answer. Question 7: State the answer you get. Question 8: Explain how you know your answer is a minimum Question 9: Compare your answers to parts i), ii), and iii). Question 10: What are the strengths and weaknesses of each