Question 194959
{{{P(x) = -2900x^2 + 7250x - 2900}}}
When an equation is of the form
{{{ax^2 + bx + c}}}, the max or min
occurs where {{{x = -b/(2a)}}}
In this case,
{{{a = -2900}}}
{{{b = 7250}}}
The maximum (in this case) occurs at
{{{x[max] = (-7250) / (2*(-2900))}}}
{{{x[max] = (-7250) / -5800}}}
{{{x[max] = 5/4}}}
The price per cup for maximum profit is $1.25
{{{P(max) = -2900x^2 + 7250x - 2900}}}
{{{P(max) = -2900*(5/4)^2 + 7250*(5/4) - 2900}}}
{{{P(max) = -4531.25 + 9062.5 - 2900}}}
{{{P[max] = 1631.25}}}
The maximum profit is $1631.25
To check this answer, both $1.24 per cup
and $1.26 per cup should give a little
less profit.
For $1.26/cup, I get $1630.96