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A firm may sell all production of a certain item at $240 per unit; producing “x” units daily, if the daily utility equation is given by the equation
u(x)= -x2 + 160x - 400.

Determine the maximum profit amount. (Dollars)

Respuesta :

Considering the vertex of the quadratic equation, the maximum profit amount is of 6,000 dollars.

What is the vertex of a quadratic equation?

A quadratic equation is modeled by:

y = ax^2 + bx + c

The vertex is given by:

[tex](x_v, y_v)[/tex]

In which:

  • [tex]x_v = -\frac{b}{2a}[/tex]
  • [tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]

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.

For this problem, the profit is modeled by:

u(x) = -x² + 160x - 400.

The coefficients are a = -1, b = 160, c = -400, and the maximum profit, in dollars, is given by:

[tex]y_v = -\frac{160^2 - 4(-1)(-400)}{-4} = 6000[/tex]

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

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