Parabola Story Problem

Question

A sales person sells an average of 45 cases when they visit 25 per week. Each time they visit an additional store per week the average sale per store decreases by one case. How many stores should they visit each week to maximize their sales?

Answer 1

x=# of additional stores and number of cases less

(45-x)(25+x)

1125-25x+45x-x²

1125+20x-x²

use -b/2a where a=-1 and b=20, (c=1125)

-20/-2=10

x=10, so 35 cases sold in each of 35 stores

if x=9...

36*34=1224 cases

if x=10...

35*35=1225 cases

if x=11...

34*36=1224 cases