The University decides to build a circular fountain on the campus.

The University decides to build a circular fountain on the campus. The school wants the fountain to be round and as large as possible but it must be restricted in a polygonal construction field, which is given by the following points: (0, 1), (0, 6), (4, 10), (8, 10), (11, 7), (11, 4), (7, 0), and (1, 0). Give a linear optimization formulation of this problem and then solve it using MATLAB or any other software. (Hint: First plot the points, and represent the polygon by using these points in the form of {x ∈ R2|aTi x ≤ bi}. Use decision variable y (center of the fountain) and the radius r.)