Question 1207286


{{{P = -0.01x^2 + 170x - 180000}}}

How many racquets should the company manufacture and sell to earn a profit of ${{{474900}}}?


{{{P=474900}}}

{{{474900 = -0.01x^2 + 170x - 180000}}}

{{{0.01x^2 - 170x + 180000+474900 =0}}}

{{{0.01x^2 - 170x + 654900 =0}}}


using quadratic formula we have


{{{x=(-(-170)+-sqrt((-170)^2-4*0.01*654900))/(2*0.01)}}}

{{{x=(170+-sqrt(28900-26196))/0.02}}}

{{{x=(170+-sqrt(2704))/0.02}}}

{{{x=(170+-52)/0.02}}}


solutions:

{{{x=(170+52)/0.02=11100}}}

or

{{{x=(170-52)/0.02=5900}}}

the company manufacture should sell {{{5900}}} or {{{11100}}} racquets to earn a profit of ${{{474900}}}