From the quadratic equation, it is found that the 2000 snowboards must be produced for the company to break even.
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The profit of producing x thousand snowboards is given by:
[tex]P(x) = 162x - 81x^2[/tex]
The break even point is the value of x for which P(x) = 0, thus:
[tex]162x - 81x^2 = 0[/tex]
[tex]81x^2 - 162x = 0[/tex]
[tex]81x(x - 2) = 0[/tex]
That has two solutions:
[tex]81x = 0 \rightarrow x = 0[/tex]
[tex]x - 2 = 0 \rightarrow x = 2[/tex]
x is in thousands, and we want the non-zero solution, thus 2000 snowboards must be produced for the company to break even.
A similar problem is given at https://brainly.com/question/24716530
