The profit(p)in dollars for a company is modeled by the function P(x) =-750*x^2+15000*x where x is the number of items produced.For which values of x will the company lose money?
P(x) = 750x(20-x)
So, since x is always positive, where do you think P(x) is negative?
To determine the values of x for which the company will lose money, we need to find the range of x where the profit (P) is negative.
The profit (P) for a company is given by the equation P(x) = -750x^2 + 15000x.
To find the values of x where the company will lose money, we need to find the roots (x-intercepts) of the equation where P(x) is less than or equal to zero.
Set P(x) = 0:
-750x^2 + 15000x = 0
Factoring out common terms, we get:
x(-750x + 15000) = 0
Solving for x, we have:
x = 0 (from the first factor)
-750x + 15000 = 0 (from the second factor)
Solving the second equation:
-750x = -15000
x = -15000 / -750
x = 20
So, there are two values of x where the company will lose money: x = 0 and x = 20.
When x = 0, it means the company is not producing any items, so there will be no profit. When x = 20, the profit becomes zero, which indicates that the company will break even or incur losses beyond this point.
Therefore, for the values x < 0 and x > 20, the company will lose money.