SOLUTION: Natalie runs a lemonade stand at the end of her driveway. She sells an average of 12 drinks each hour at $25 a glass. For each $2 decrease in the price, her sales increase by 3 dri

Question 1051963: Natalie runs a lemonade stand at the end of her driveway. She sells an average of 12 drinks each hour at $25 a glass. For each $2 decrease in the price, her sales increase by 3 drinks per hour. At what price per drink will she make the most money? How much will she receive?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Let h be the number of hours, then
:
1) (25-2h) * (12+3h) = total amount made in h hours (T)
:
-6h^2 +51h +300 = T
:
The graph of this function is a parabola that curves downward, we want the
coordinates of the vertex of the parabola
:
x value = -b / 2a = -51 / (2*(-6)) = 4.25
:
substitute x value for h in equation 1)
:
-6(4.25)^2 +51(4.25) + 300 = 408.375 approx 408.38
:
*********************************************
25 - 2(4.25) = 16.50
:
She receives the most money at $16.50 / glass
:
She receives $408.38
*********************************************
:

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