(2 marks) Solve (find the optimal point and objective function value at the optimal point) the following optimisation problem min 2x+ y Subject to Obtain the gradient of both the objective function and constraint function at the optimal point. What condition do they meet at the optimal point? Suppose the right-hand side of the constraint equation is increased from 1 to 1.2. Without redoing the Lagrange multiplier method obtain an estimate for the change in objective function value. Verify using the bordered Hessian second order conditions that the solution you obtained is indeed a minimum point. Verify that this is a convex optimisation problem.
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