What is the extreme G(x,y)=40000x+30000y-8x^2-15y^2-10xy ?

The extreme G(x,y)=40000x+30000y-8x^2-15y^2-10xy is Maximum(45000/19 , 4000/19)

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extreme G(x,y)=40000x+30000y-8x^2-15y^2-10xy

extreme

Maximum (\frac{45000}{19}, \frac{4000}{19})

Solution steps

Find the critical points:

(\frac{45000}{19}, \frac{4000}{19})

\frac{\partial ^{2} f}{\partial x ^{2}} = - 30

D (x, y) = 380

Check the sign of at each critical point

Check critical point

(\frac{45000}{19}, \frac{4000}{19}) :

Maximum

Maximum (\frac{45000}{19}, \frac{4000}{19})

What is the extreme G(x,y)=40000x+30000y-8x^2-15y^2-10xy ?
The extreme G(x,y)=40000x+30000y-8x^2-15y^2-10xy is Maximum(45000/19 , 4000/19)