Find the extremum of f(x, y) subject to the given constraint, and state whether it is a maximum or a minimum.
f ( x, y )=2 x^2 +3y^2 - 4 xy; x+ y =27
there is a minimum value of 162 located at (x, y)=( 15,12 ).

The Lagrangian is

with critical points whenever

Solving for and , we get

so there is one critical point at (15, 12), at which point .

The Hessian matrix for this function is

with determinant 8 > 0, and , which tells us this point is a minimum.

15% chance.

step-by-step explanation:

3/10 times, the 5 year old will get a tablet. 5/10 times, the 13 yer old will get a tablet. multiply both fractions to get 15/100 times, both would have a tablet.