Question 195688
{{{P(x)= -2900x^2 + 7250x - 2900}}}
When the equation is in the form
{{{ax^2 + bx + c}}}, the max or min
of the function occurs at:
{{{x[max] = -b/(2a)}}} (max in this case)
{{{x[max] = -7250 / (2*(-2900))}}}
{{{x[max] = 7250 / 5800}}}
{{{x[max] = 1.25}}}
At maximum profit, the price per cup is $1.25
And to find the maximum profit:
{{{P(x)= -2900x^2 + 7250x - 2900}}}
{{{P(1.25)= -2900*1.25^2 + 7250*1.25 - 2900}}}
{{{P(1.25)= -4531.25 + 9062.5 - 2900}}}
{{{P(1.25)= -4531.25 + 9062.5 - 2900}}}
{{{P(1.25) = 1631.25}}}
The maximum profit is $1,631.25
I'll plot to check this:
{{{ graph( 600, 600, -5, 3, -200, 1800, -2900x^2 + 7250x - 2900) }}}
Looks like I could be right