Question 1194915
x is number of steps of change
(300-40x)(3.50+0.25x)
=1050-140x+75x-10x^2
or x, the number of steps, is -10x^2-65x+1050.
The maximum for this is when x=-b/2a or 65/-20 or -3.25 steps, so the price should be dropped.
This can be checked 
300*$3.50=$1050 right now
260*$3.75=975 raising
340*3.25=$1105.
The price should be decreased  3.25 *$0.25=$0.8125 to $2.6875
the number will then increase to 3.25*40 or 130 more or 430 lattes
this maximum revenue is $1155.625 or $1155.63  Ordered pair is (430, 2.6875)
Can check this by looking at 420 lattes which would be (420, 2.75) and revenue of $1102.50
and the other direction with 440 lattes and price $2.625 and revenue of $1155.
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The function N(p) is linear. If p is 0, this represent 14 25 cent steps more than the current 300 lattes, or 560 more people. The y-intercept (N) is 860 and the slope is 0.25/-40 or -0.0625 or in dollars 1/-160
N=860-160p, where p is in dollars. At a price of 860/160 or $5.375, no lattes would be sold.
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Revenue R(p)=Number * price=(860-160p)*p
{{{graph(300,300,-3,6,-100,1700,(860-160x)*x)}}}