Question 1060581
r, income
x, how many pails sold
p, price per pail
{{{r=px}}}


n, each dollar decrease in price
<pre>
PRICE    x
 20      80
 20-1    80+15
 20-2    80+2*15
 20-3    80+3*15
 20-n    80+n*15 or 80+15n
</pre>

{{{highlight(r=(20-n)(80+15n))}}}


r is a parabolic function with zeros at  {{{(20-n)(80+15n)=0}}}, and the MAXIMUM revenue will be exactly in the middle of the two zeros for n.


--
{{{20-n=0}}}
{{{n=20}}}
-
{{{80+15n=0}}}
{{{15n=-80}}}
{{{n=-80/15}}}
{{{n=-5&1/3}}}
-
MIDDLE n VALUE
{{{(20-5&1/3)/2}}}
{{{highlight(n=7&1/3)}}}----------how many dollars LESS THAN 20, for maximum revenue.


If Jack and Jill want a price to the nearest penny, then this would be $7.33 per pail.
Revenue would be  {{{r=7.33(80+7.33*15)=highlight(1392.33)}}}.