An engineer is designing a bridge over an inlet, with the aim to minimize the length of the bridge (think about the Second Narrows bridge here in Vancouver). The bridge is defined by the coordinates of its extremities, (, y) for the south extremity and (2, 32) for the north extremity. Near where it is to be located the shorelines can be represented by the graph of the functions y (x)=-e- and Y(x) = 1 + x where y, is the south shoreline and y/2 the north one. a) Sketch the problem, i.e. draw an abstract sketch of the problem the negineer wants to solve, indicating what the unknowns are and how many there are. b) Write down a minimization problem to find the coordinates of the extremities of the bridge. c) She (the engineer) writes a code to solve the problem numerically. First, she tests with y(x) = 0 and 32(x) = 1 + x. What is the solution in this case? Explain your answer. d) Run the code h1_q3.m to verify it provides your answer to part c). Now modify the code to find the true answer with y(x) = -e-. e) (For 2 extra marks). Augment the provided Matlab code to plot a colormaped contour of the function defining the length of the bridge as a function of the x-coordinates of its extremities. I intentionally do not provide hints for this question to have you practice to find novel commands in Matlab.