SOLUTION: Min y Kısıtlar x^2 + y^2 ≤ 4 x^2 ≥ 1 yukarıdaki doğrusal olmayan kısıtlı model için olurlu bölgeyi x ve y eksenlerini kullanarak çiziniz ve çizdiğiniz grafiğ

Question 1182172: Min y
Kısıtlar x^2 + y^2 ≤ 4
x^2 ≥ 1
yukarıdaki doğrusal olmayan kısıtlı model için olurlu bölgeyi x ve y
eksenlerini kullanarak çiziniz ve çizdiğiniz grafiği kullanarak optimum
değer(ler)i bulunuz.
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!

We translate from Turkish to English, and
we use x for x₁ and y for x₂.

Minimize y subject to the constraints



For the nonlinear constrained model above, plot the feasible region using
the x and y axes and find the optimum (minimum) value(s) using the graph you
drew.

We draw the boundary graphs, replacing the ≤ and ≥ by =



Their graphs are the circle with radius 2, and the two vertical lines at 
x = 1 and x = -1. 



We find the points of intersection of the graphs:










The four points of intersection are:






Then the feasible region is:



From the graph, the minimum value of y is 

Edwin

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