tonesfairy
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The profit from a business is
described by the function
P(x) = -5x² + 30x + 8, where x
is the number of items made,
in thousands, and P(x) is the
profit in dollars. How many
items will maximize the profit?

The profit from a business is described by the function Px 5x 30x 8 where x is the number of items made in thousands and Px is the profit in dollars How many it class=

Respuesta :

Kpopgirlie

First of all we will understand the question!!

The question is saying that you are given a function and you have to find the value of x which will give the maximum profit... Lets solve it by finding the extrema using the vertex

[tex] \rm \: p(x) = - 5 {x}^{2} + 30x + 8[/tex]

  • Identify the coefficients a and b of the quadratic function

[tex] \rm \: p(x) = { - 5x}^{2} + 30x + 8 \\ \rm \: a = - 5 \: and \: b \: = 30[/tex]

  • Since a<0, the function has the maximum value at x, calculated by substituting a and b into x=-b/2a

[tex] \rm \: x = \frac{30}{ 2 \times (- 5)} [/tex]

  • Solve the equation for x

[tex] \rm \: x = 3[/tex]

  • The maximum of the quadratic function is at x=3

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