What is the extreme G(x,y)=50000x+40000y-10x^2-20y^2-10xy ?

The extreme G(x,y)=50000x+40000y-10x^2-20y^2-10xy is Maximum(16000/7 , 3000/7)

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extreme G(x,y)=50000x+40000y-10x^2-20y^2-10xy

extreme points

G (x, y) = 50000 x + 40000 y - 10 x^{2} - 20 y^{2} - 10 x y

Maximum (\frac{16000}{7}, \frac{3000}{7})

Solution steps

Find the critical points:

(\frac{16000}{7}, \frac{3000}{7})

\frac{\partial ^{2} f}{\partial x ^{2}} = - 40

D (x, y) = 700

Check the sign of at each critical point

Check critical point

(\frac{16000}{7}, \frac{3000}{7}) :

Maximum

Maximum (\frac{16000}{7}, \frac{3000}{7})

f (x) = x^{2} - 5 x + 4

f (x, y) = 5 x^{4} - x^{2} + 3 y^{2}

x + 2 + 1

y e^{x^{2} - 2 y^{2}}

f (x) = 2 - 2 cos (x), (0, 2 π)

What is the extreme G(x,y)=50000x+40000y-10x^2-20y^2-10xy ?
The extreme G(x,y)=50000x+40000y-10x^2-20y^2-10xy is Maximum(16000/7 , 3000/7)