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Question 113309: A salesperson finds that her sales average 40 cases per store when she visits 20 stores per week. For every two additional stores she visits per week, the average sales per store decrease by one case. How many stores should she visit each week if she wants to maximize her total sales?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A salesperson finds that her sales average 40 cases per store when she visits 20 stores per week. For every two additional stores she visits per week, the average sales per store decrease by one case. How many stores should she visit each week if she wants to maximize her total sales?
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Chart:
If # of stores=20, sales per store = 40, and total sales = 20*40 = 800
If # of stores = 20+2*1, sales perstore = 40-1, and total sales =(20+2)(40-1)
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If # of stores = 20+2x, sales per store = 40-x, and total sales = (20+2x)(40-x)
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EQUATION:
Total sales = (20+2x)(40-x)
Ts = 800+60x-2x^2
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Maximum occurs when x=-b/2a = -60/(2*-2) = 15
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She should visit 20+2*15 = 50 stores per week to maximize sales.
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Cheers,
Stan H.
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