Using the vertex of the quadratic equation, it is found that the company should assign 5 programmers in order to complete the development as quickly as possible.
What is the vertex of a quadratic equation?
A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
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.
In this problem, the time needed for x programmers to finish the project is given by:
T(x) = 100 - 30x + 3x².
Which means that the coefficients are a = 3, b = -30, c = 100. The number of programmers which will minimize the time is given by:
[tex]x_v = -\frac{-30}{6} = 5[/tex]
More can be learned about the vertex of a quadratic equation at https://brainly.com/question/24737967
