Find the rectangle with maximal area which can be cut from an elliptical plate (see the figure
below). The long axis of the ellipse is 3 meters and the short axis is 1 meter, so the equation of
the ellipse is given by ( x^2 )/9  + y^2 =1

 

(1) Develop the mathematical model of the optimisation problem;
(2) Solve the problem using Lagrange Multiplier method.
(3) Use MATLAB fmincon or Excel solver to solve the problem.
 

y X