Question

# 4. You are building a new walking track in Providence, above the city. The company that...

4. You are building a new walking track in Providence, above the city. The company that hired your team gave you a basic idea of the track shape they were interested in, but told your team to just ensure the area was maximized to give walkers a great view of the city: x

a. Find a formula for the area enclosed by the track, using x and y as your only variables (as pictured). Simplify your answer as much as possible. (Hint: you may want to break the track into a few shapes to find the area).

b. Find a formula for the perimeter of the track. Simplify your answer as much as possible.

c. Find the dimensions of both x and y that maximize the area (I suggest trying to find your y value first and do not round your answers until the very end), given that the total perimeter of the track is 950 meters. You must use optimization methodology to solve this problem and you must show that this is a maximum. (Round your answer to 5 decimal places, if necessary).

d. Determine the maximum area. (Round your answer to 3 decimal places, if necessary).

***I need this question answered with calculus and derivatives. The other solutions are not right for my class****

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