in a class of 15 boys and 35 girls 40% of the students in the class take the bus to school how many students do not take the bus
1 answer:
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The Lagrangian for this function and the given constraints is
which has partial derivatives (set equal to 0) satisfying
This is a fairly standard linear system. Solving yields Lagrange multipliers of
and 
, and at the same time we find only one critical point at 
.
Check the Hessian for
, given by
is positive definite, since 
for any vector 
, which means 
attains a minimum value of 
at 
. There is no maximum over the given constraints.
which has partial derivatives (set equal to 0) satisfying
This is a fairly standard linear system. Solving yields Lagrange multipliers of
Check the Hessian for