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?
Find x
To find the value of x that will lead to the maximum profit, we need to find the vertex of the quadratic equation represented by the profit function.
The vertex of a quadratic equation in the form of ax^2 + bx + c can be found using the formula x = -b / (2a).
In this case, a = -5 and b = 1000. Plugging these values into the formula, we get:
x = -1000 / (2*-5)
x = -1000 / -10
x = 100
Therefore, spending $100,000 on marketing will achieve the maximum profit.
Wrong
Apologies for the mistake.
To find the amount of spending that will achieve the maximum profit, we need to find the vertex of the quadratic equation represented by the profit function.
The profit function is given by P = -5x^2 + 1000x + 5000.
The x-coordinate of the vertex can be found using the formula x = -b / (2a), where a = -5 and b = 1000.
x = -1000 / (2*(-5))
x = -1000 / (-10)
x = 100
Therefore, spending $100,000 on marketing will achieve the maximum profit.
Change reply
Apologies once again for the previous incorrect response.
The profit function is given by P = -5x^2 + 1000x + 5000.
To find the amount of spending that will achieve the maximum profit, we can use the formula for the x-coordinate of the vertex, which is given by x = -b / (2a), where a = -5 and b = 1000.
x = -1000 / (2*(-5))
x = -1000 / (-10)
x = 100
Therefore, to achieve the maximum profit, the company should spend $100,000 on marketing.