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Can you guide me on how to solve this exercise? I need your help please. I don't understand the correct way to do it. being a nonlinear programming problem. can it be solved by simplex method? or the simplex method only applies to linear optimization? Can you tell me the step by step of this exercise?

minimize $ x^2_1- x_1 x_2+ 2x^2_2-4x_1 -5x_2 $

$x_1 + 2x_2≤6$

$ x_1≤2$

$x_1≥0 , x_2 ≥0$

a) solve the problem geometrically.

b) verify the optimality of the function by the Kuhn - Tucker conditions

angelabayona
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  • I would sketch the constraints and draw the level sets of the cost (which are ellipses). – copper.hat Sep 23 '22 at 21:08
  • I don't usually recommend this sort of approach, but Desmos might help. – copper.hat Sep 23 '22 at 21:10
  • Do you know how to solve (a) the unconstrained minimization problem? (b) do you know whether the objective function is a convex function? If you have difficulties in answering any of these questions... you really need to study more basic stuff related optimization before solving a problem like this. – bluemaster Sep 23 '22 at 22:28
  • Hello, you can clarify this question, when it claims to interpret the problem geometrically what it refers to? Is it to graph the problem? I do not understand, if you can clarify this I will be very grateful – angelabayona Sep 30 '22 at 16:01

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