Question

Elliot makes and sells key chains. His profit depends on what price he charges for a key chain. He writes the expression (1 - 10) (60 - 3x) to represent his profit based on the price per key chain, I. Profit (S) 40+ 20+ Use the drop-down menus to complete the statements about Elliot's profit.​

Answer 1

Using the vertex of the quadratic function, it is found that his maximum profit is of $75 when he charges $15 for a key-chain.

What is the vertex of a quadratic equation?

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.

In this problem, the function is:

$f(x) = (x - 10)(60 - 3x)$

In standard format, it is given by:

$f(x) = -3x^2 + 90x - 600$

Which means that it's coefficients are a = -3, b = 90, c = -600.

Hence:

$x_v = -\frac{90}{2(-3)} = 15$

$y_v = -\frac{90^2 - 4(-3)(-600)}{4(-3)} = 75$

Hence, his maximum profit is of $75 when he charges $15 for a key-chain.

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