SOLUTION: A salesperson finds that her sales average 30 cases per store when she visits 20 stores a week. Each time she visits an additional store per week, the average sales per store decre
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Question 1059034: A salesperson finds that her sales average 30 cases per store when she visits 20 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? Found 3 solutions by Boreal, addingup, josmiceli:Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! Want to maximize the function (30-x)(20+x)=600+10x-x^2
or x^2-10x-600=0
vertex is maximum and occurs at -b/2a or 10/2=5 for x
She would want to visit 25 stores and sell 25 cases for a maximum of 625.
You can put this solution on YOUR website! Let y = her total sales (in cases).
Let x = the number of ADDITIONAL stores she visits (beyond the 20 she starts at).
:
y = (20+x)(30-1x)
Let's expand this equation (First, Outer, Inner, Last):
y = -1x^2+20x+600
This is a parabola, and we want to find its maximum. If you are in calculus you could use the derivative. But here's in case you are not taking calculus right now:
The x-coordinate of the vertex of a quadratic in the form y = ax^2+bx+c can be found by the equation:
:
x = (-b}/(2a)
Since we only need to find out how many stores she should visit, we are only concerned with x:
:
x = (-20}/{-2} = 10 She should visit 10 ADDITIONAL stores per week
You can put this solution on YOUR website! Let = the number of additional stores/week she visits
Let = her average sales in cases/week
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In terms of units, this is:
[ cases/week ] = [ stores/week ] x [ cases/store ]
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I have to maximize
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Use the formula for of the vertex
of the parabola
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Note that is the ADDITIONAL number of
of stres she should visit per week is the total number of store she should visit
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She should visit 25 stores/week to maximize profit
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Here's the plot of the equation:
