Respuesta :
Answer:
The maximum possible daily profit is $11,500.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, f(x_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]f(x_{v})[/tex]
In this question:
The maximum daily profit happens when [tex]x_{v}[/tex] cars are sold. This profit is [tex]P(x_{v})[/tex]
[tex]P(x) = -35x^{2} + 2100x - 20000[/tex]
So [tex]a = -35, b = 2100[/tex]
[tex]x_{v} = -\frac{2100}{2*(-35)} = 30[/tex]
The maximum possible daily profit is:
[tex]P(30) = -35*30^2 + 2100*30 - 20000 = 11500[/tex]
The maximum possible daily profit is $11,500.
