Question

A company sells widgets the amount of profit y made by the company is related to the selling price of each Widget x by the given equation using the equation find out the maximum amount of profit the company can make to the nearest dollar

Answer 1

Quadratic Function

Given a quadratic function of the form:

`y=ax^2+bx+c`

The vertex of the parabola that represents the function is located at the x-coordinate:

`x=-(b)/(2a)`

If the value of a is positive, the function has a minimum value at the vertex and if a is negative, the function has a maximum value at the vertex.

We are given the amount of profit y, as a function of the selling price of each widget x:

`y=-2x^2+105x-773`

Here: a=-2, b=105, c=-773. Calculating the x-coordinate of the vertex:

`x=-(105)/(2\cdot(-2))=(105)/(4)=26.25`

Now substitute in the function:

`y=-2(26.25)^2+105\cdot26.25-773=605.125`

The maximum amount of profit the company can make is $605