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 x 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?(1 point)
To find the amount of spending that will achieve the maximum profit, we need to find the x-coordinate of the vertex of the parabola represented by the profit function.
The x-coordinate of the vertex is given by the formula x = -b / (2a), where the equation of the parabola is in the form y = ax^2 + bx + c.
In this case, a = -5, b = 1000, and c = 5000. Plugging these values into the formula, we have:
x = -(1000) / (2*(-5))
x = -1000 / (-10)
x = 100
Therefore, spending $100,000 (in thousands) on marketing will achieve the maximum profit.