An oil drilling rig located 14 miles off of a straight coastline is to be connected by a pipeline to a refinery 10 miles down the coast from the point directly opposite the drilling rig. Use calculus to solve and justify your answers to the questions below. Round mileage values to at least 4 decimal places. Round currency values to 2 decimal places. Be sure to justify your answers.   (a) Assume that laying underwater pipe costs twice as much as laying pipe on land. What path should the pipe take in order to minimize the total cost of the pipeline? What is the minimum cost if pipe costs $60,000 per mile on land?     (b) Suppose that underwater pipe costs 1.4 times as much as land pipe. What path should the pipe take? Hint: reconsider your picture     c) Suppose that underwater pipe costs α times as much as pipe on land ( α >1). Which combination of underwater and land-based pipe will minimize the total cost of the pipeline now? (Write your answer in terms of α.)

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.