Use the Lagrange multipliers approach and determine the optimized perimeter of the following shape made up of a rectangular section and a circular section as shown in the figure. Only the positive values of "a" and "b" are valid, then, lambda must be negative in case it is the square root of a value (take the negative solution for lambda). The area of the shape must be 1,152 squared inches

What is the value of "a" in inches for ther optimized perimeter?

y(in) a b x(in) y(in) a b x(in)