Answer:
The maximum amount of profit the company can make is of $1577.
Step-by-step explanation:
The profit is given by the following equation:
[tex]y = -2x^2 + 145x - 1051[/tex]
Which is a quadratic equation.
Maximum value of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]y = ax^2 + bx + c, a < 0[/tex]
The maximum value of the function is given by:
[tex]y_{MAX} = \frac{-(b^2-4ac)}{4a}[/tex]
In this question, we have that:
[tex]a = -2, b = 145, c = -1051[/tex]. So
[tex]y_{MAX} = \frac{-(b^2-4ac)}{4a}[/tex]
[tex]y_{MAX} = \frac{-(145^2-4(-2)(-1051))}{4(-2)}[/tex]
[tex]y_{MAX} = 1577.125[/tex]
To the nearest dollar, $1577
The maximum amount of profit the company can make is of $1577.
