A salesperson finds that her sales averages 40 cases per store when she visits 20 stores per week. If she visits an additional store per week, her avg. sales per store decrease by one case. How many stores per week should she visit to maximize her sales?

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Answer 1 · 2016-10-13T20:50:10

#30# stores.

#P = "number of stores" xx "cases/store"#

Let #x# be the number of increases that she does in the number of stores she visits.

#P = (20 + x)(40 - x)#

#P = 800 + 20x - x^2#

The maximum profit will occur at the vertex of this function. Hence, we should complete the square to convert to vertex form.

#P = -(x^2 - 20x) + 800#

#P = -(x^2 - 20x + 100 - 100) + 800#

#P = -(x - 10)^2 + 100 + 800#

#P = -(x - 10)^2 + 900#

#:.# She should visit #20 + 10 = 30# stores to maximize her sales.

Hopefully this helps!