Question

A beekeeper’s hives are making honey at a constant rate. The profit from honey can be represented by the equation

Answer 1

Using the vertex of a quadratic function, she should harvest her honey after 64 days to maximize profit.

What is the vertex of a quadratic equation?

A quadratic equation is modeled by:

$y = ax^2 + bx + c$

The vertex is given by:

$(x_v, y_v)$

In which:

• $x_v = -\frac{b}{2a}$

• $y_v = -\frac{b^2 - 4ac}{4a}$

Considering the coefficient a, we have that:

• If a < 0, the vertex is a maximum point.

• If a > 0, the vertex is a minimum point.

The profit function is given as follows:

P(t) = -16t² + 2050t + 150.

The coefficients are a = -16 < 0, b = 2050, c = 150, hence the t-value of the vertex is:

$t_v = -\frac{b}{2a} = -\frac{2050}{-32} = 64$

Hence she should harvest her honey after 64 days to maximize profit.

More can be learned about the vertex of a quadratic function at brainly.com/question/24737967

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