Here you go!! Solved step by step with work shown!! :))
Number of people: 80
Number of Men: 47
Number of Women: 33
Ratio that best represents the number of men and the number of women:
47 : 33
has critical points where the partial derivatives simultaneously vanish:
So we have three critical points to consider,
,
, and
.
The function has Hessian
At the critical points, we have
which means there is a minimum at (0, 0) of
;
which means
is a saddle point; and
which means
is also a saddle point.
Subtracting 3.25 hours from 10 PM is subtracting 3 hours and 15 minutes from 10 PM. Doing this, we get that the game started at 6:45 P.M. Hope this helped!