Question 1174921
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<pre>

    P(x) = −2x^2 + 38x − 120 = -2*(x^2 - 19x + 60) = -2*(x - 4)(x-15)


    P(4) = 0  and P(15) = 0     4 ≤  x  ≤ 15   will either break even or show a profit

    
    P(9.5) shows the maximum profit.



    {{{drawing(300, 300,   -25, 25, -20, 80,  blue(line(9.5, 80,  9.5, -20)) ,  
               grid(1),
       graph( 300, 300,    -25, 25, -20, 80, -2x^2 +38x - 120 ))}}}

</pre>   


Find several important differences from the post by @ewatrrr.