Question 1100684
{{{ P(x) = -5x^2 + 8x + 5 }}}
The x-value of the peak ( max profit ) is:
{{{ x[max] = -b/(2a) }}}
{{{ a = -5 }}}
{{{ b = 8 }}}
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{{{ x[max] = -8/(2*(-5)) }}}
{{{ x[max] = 8/10 }}}
{{{ .8*1000 = 800 }}}
800 speakers should be sold
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check:
Here's the plot
Plug {{{ x = .8 }}} back into equation to get {{{ P[max] }}}
{{{ graph( 400, 400, -1, 2, -1, 10, -5x^2 + 8x + 5 ) }}}