Question 953095
{{{ C(x) = 2x^2 - 800x + 92000 }}}
{{{ C(x) = x^2 - 400x + 46000 }}}
The minimum value of {{{ x |}}} is
given by:
{{{ x[min] = -b/(2a) }}}
where:
The equation has the form:
{{{ C(x) = a*x^2 + b*x + c }}}
{{{ a = 1 }}}
{{{ b = -400 }}}
{{{ x[min] = -(-400)/(2*1) }}}
{{{ x[min] = 400/2 }}}
{{{ x[min] = 200 }}}
The minimum {{{x}}} is 200
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{{{ C(x) = x^2 - 400x + 46000 }}}
{{{ C(200) = 200^2 - 400*200 + 46000 }}}
{{{ C(200) = 40000 - 80000 + 46000 }}}
{{{ C(200) = -40000 + 46000 }}}
{{{ C(200) = 6000 }}}
The minimum cost is $6,000
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Check:
Here's the plot:
{{{ graph( 400, 400, -80, 400, -5000, 50000, x^2 - 400x + 46000 ) }}}