Please help PreCalculas Q?
A salesperson finds that her sales average 60 cases per store when she visits 5 stores a week. Each time she visits an additional store per week, the average sales per store decreases by 4 cases. How many stores should she visit each week if she wants to maximize her sales?
.........stores
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For each additional store sales drop by 4.
Let y= Total sales
Let x= number of additional stores.
y =(60-4x)(5+x) - (you can see here that if I add one store average revenue drops by $4 and the store count goes up by 1. )
y = 300 + 40x - 4x^2
Maximum total sales occur when dy/dx =0
dy/dx=40-8x
0 = 40 - 8x
-40 = -8x
5 = x
Note x = additional stores.
We started out with 5 stores
so ( 5 +x ) = Total number of stores
Therefore 5 +5 = 10 stores.
MAXIMUM SALES WILL OCCUR AT 10 STORES
( Note: you can check to see that is the case by looking at one store above and below this point)