How to find the vertex through this word problem?

Question

A salesperson finds that her sales average 40 cases per store when she visits 30 stores a week. Each time she visits an additional store per week, the average sales per store decreases by 1 case. How many stores should she visit each week if she wants to maximize her sales?

Answer 1

let x=# of stores and the number of cases

40*30=1200 cases

(30+x)(40-x)=0

1200+40x-30x-x²=0

1200+10x-x²=0

this is a parabola with a maximum point, the vertex

vertex=(h,k)

h=-b/2a

h=-10/-2=5 stores she should visit

(30+5)(40-5)=35*35=1225 cases

if she visited 4 stores: 34*36=1224 cases

if she visited 6 stores: 36*34=1224 cases

vertex=(5,1225)