document.write( "Question 1089043: A salesperson finds that her saStules average 40 cases per store when she visits 30 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?\r
\n" ); document.write( "\n" ); document.write( "It is asking for the vertex I think. \n" ); document.write( "

Algebra.Com's Answer #703405 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
They are really asking for the x-coordinate (or the axis of symmetry for the quadratic function total sales as function of number of stores visited.
\n" ); document.write( "Hulu are told average sales per store, $\"a\"$ , is a linear function of $\"x\"$ (number of stores visited).
\n" ); document.write( "It is $\"a-40=-1%28x-30%29\"$ <---> $\"a=-x%2B70\"$ ,
\n" ); document.write( "with a slope of $\"-1\"$ , and
\n" ); document.write( "going through the point with $\"a=40\"$ for $\"x=30\"$ .
\n" ); document.write( "Total sales is given by
\n" ); document.write( " $\"y=a%2Ax\"$ or $\"y=%28-x%2B70%29x\"$ ---> $\"y=-x%5E2%2B70x\"$ .
\n" ); document.write( "The vertex is a maximum an happens for $\"x=%28-70%29%2F%282%28-1%29%29=35\"$ . \n" ); document.write( "

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