Question: A round billboard with radius R = 55 in. is designed to have a rectangular picture placed inside a rectangle with sides a and b.

A round billboard with radius R = 55 in. is designed to have a rectangular picture placed inside a rectangle with sides a and b. The margins between the rectangle and the picture are 10 in. at the top and bottom and 4 in. at each side. Write a MATLAB program that determines the dimensions a and b such that the overall area of the picture will be as large as possible. In the program define a vector a with values ranging from 5 to 100 with increments of 0.25. Use this vector for calculating the corresponding values of b and the overall area of the picture. Then use MATLAB's built-in function max to find the dimensions of the largest rectangle.

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