Using the vertex of the quadratic equation, it is found that:
The revenue is at maximum after 19.33 hearing aids are produced and sold. The maximum revenue is $1121.33.
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The definition of a quadratic function is:
[tex]y = ax^2 + bx + c[/tex]
It's vertex is:
[tex](x_v, y_v) = (-\frac{b}{2a}, -\frac{b^2 - 4ac}{4a})[/tex]
The revenue is defined by:
[tex]R(x) = -3x^2 + 116x[/tex]
Which is a quadratic equation with [tex]a = -3, b = 116, c = 0[/tex]
Thus, the vertex is:
[tex]x_v = -\frac{b}{2a} = -\frac{116}{2(-3)} = 19.33[/tex]
[tex]y_v = -\frac{b^2 - 4ac}{4a} = -\frac{116^2}{4(-3)} = 1121.33[/tex]
The revenue is at maximum after 19.33 hearing aids are produced and sold. The maximum revenue is $1121.33.
A similar problem is given at https://brainly.com/question/24626341
