Yes I think that is what you do but others can elaborate more im sure
The Lagrangian is

with partial derivatives (set equal to 0)





Case 1: If
, then

Then


So we have two critical points,
and 
Case 2: If
, then in the first equation we get

and from the third equation,

Then


but there are no real solutions for
, so this case yields no additional critical points.
So at the two critical points we've found, we get extreme values of
(min)
and
(max)
Answer:
$226.57
Step-by-step explanation:
1. Subtract $48.73 from $317.89
2. Now you have $269.16 so subtract $10.13 from it
3. You should have $259.03 so subtract $32.46 from it
4. Finally you should get $226.57