The profit ( in thousands of dollars) of a company is represented as P = -5x^2 + 1,000x +5,000, where P represents the profit and c represents the amount spent on marketing( in thousands of dollars). How much spending in the thousands will be directed toward marketing to achieve the maximum profit
To find the amount of spending that will achieve the maximum profit, we need to determine the x-coordinate of the vertex of the quadratic function.
The x-coordinate of the vertex can be found using the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic function in the standard form ax^2 + bx + c.
Comparing the given quadratic function P = -5x^2 + 1,000x + 5,000 with the standard form, we have a = -5 and b = 1,000.
Using the formula x = -b/2a, we can calculate the x-coordinate of the vertex as:
x = -1,000 / (2 * -5)
x = -1,000 / -10
x = 100
Therefore, spending $100,000 (in thousands) on marketing will achieve the maximum profit.