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.
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)
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