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Vedmedyk [2.9K]
2 years ago
10

NEED HELP ASAP 1 HOUR LEFT

Mathematics
1 answer:
katen-ka-za [31]2 years ago
6 0

Using the vertex of a quadratic function, it is found that:

a) The revenue is maximized with 336 units.

b) The maximum revenue is of $56,448.

<h3>What is the vertex of a quadratic equation?</h3>

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 demand function is given by:

p(x) = 336 - 0.5x.

Hence, the revenue function is:

R(x) = xp(x)

R(x) = -0.5x² + 336x.

Which has coefficients a = -0.5, b = 336.

Hence, the value of x that maximizes the revenue, and the maximum revenue, are given, respectively, as follows:

  • x_v = -\frac{336}{2(-0.5)} = 336
  • y_v = -\frac{336^2 - 4(-0.5)(0)}{4(-0.5)} = 56448

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

#SPJ1

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