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?
To find the amount of spending in thousands that will result in the maximum profit, we need to determine the x-coordinate of the vertex of the given quadratic equation.
The quadratic equation is given as P = -5x^2 + 1000x + 5000.
To find the x-coordinate of the vertex, we can use the formula x = -b / (2a), where a and b are the coefficients of the quadratic equation in the form ax^2 + bx + c.
In this case, a = -5 and b = 1000. Plugging these values into the formula, we get x = -1000 / (2 * -5) = 1000 / 10 = 100.
Therefore, spending $100,000 in marketing will achieve the maximum profit.