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1. A rectangle with its one side on the x-axis and the opposite corners bounded by a curve y = 10 - x2 as shown

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1. A rectangle with its one side on the x-axis and the opposite corners bounded by a curve y = 10 - x2 as shown in the figure. Formulate an optimization problem for the maximum areaFind the dimensions of the rectangle and its corresponding area. a. Formulate an optimization problem for the maximum area. b. Write the necessary and sufficient conditions for the optimal solution in the context of the given problem c. Find the dimensions of the rectangle and its corresponding area

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