Final answer:
To determine the maximum profit a company can make, you need to find the vertex of the quadratic function. In this case, the maximum profit is $93,250.
Step-by-step explanation:
In this quadratic equation, P(x) = -5x² + 1400x - 2550, represents the profit function of a company.
To determine the maximum profit the company can make, we need to find the vertex of the quadratic function. The vertex of a quadratic function in the form ax² + bx + c can be found using the formula x = -b/2a.
By substituting the values a = -5 and b = 1400 into the formula, we can calculate the x-coordinate of the vertex. Once we have the x-coordinate, we can substitute it back into the original equation to find the maximum profit.
Calculations:
x = -1400 / (2 * -5) = 1400 / 10 = 140
P(140) = -5(140)² + 1400(140) - 2550 = -5(19600) + 196000 - 2550 = -98000 + 196000 - 2550 = 93250
The maximum profit the company can make is $93,250.