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Problem 1: Sensitivity Analysis Start with the takeoff weight equation: Wo = Whuman +W payload 1- Wempty fuel Wo Wo Assume you've already worked out the following parameters and correlations for a jet transport aircraft: Whuman = 400 lbs Wpayload = 2500 lbs R = 600 miles Wempty = 0.32 + 0.9035 . W -0.13 (Wo in lbs) Wo W fuel = 1.06 1 - 0.934 . exp -R (R in miles) Wo 8839 a. Iteratively calculate the aircraft's initial weight Wo. Use a starting guess of 10,000 lbs. Using a computer is advised; no need to show all your code. b. Numerically calculate the performance partial derivatives for payload weight and range, i.e. awo awo (Hint: This will require more iterative calculations.) aw payload OR c. Use the performance partial derivatives from part (b) to solve the following: To increase the aircraft's range by 100 miles without changing the takeoff weight, by how much would you need to reduce the payload weight