x 1500x 20x2 xy y 3300y 10y2 5xy find the critical pointsS

x\' = 1500x -20x^2 -xy

y\' = 3300y -10y^2 -5xy

find the critical points

Solution

Critical points are points where

x\'=y\'=0

x\'=0 gives

1500x-20x^2-xy=0

x(1500-20x-y)=0

x=0, 1500=20x+y

3300y-10y^2-5xy=0

y(3300-10y-5x)=0

y=0,3300=10y+5x

y=0,660=2y+x

So, (0,0) is one critical point

Other critical point is obtained by solving the two linear equations

660=2y+x,1500=20x+y

Solving gives

(60,300) as other critical point