Question
the inventory (the number of item in supply less the items ordered but not yet shipped) of a popular product in the month of December is represented by the function below where x is the number of days into the month
g(x)=x^2-16x-225
during which interval will the product be on back order (negative inventory)?
g(x)=x^2-16x-225
during which interval will the product be on back order (negative inventory)?
Answers
GPT 3.5
To find when the product is on back order (negative inventory), we need to set the function g(x) less than zero:
x^2 - 16x - 225 < 0
Now, we need to solve for x by factoring the quadratic:
(x - 25)(x + 9) < 0
From this, we can see that the solutions are x = 25 and x = -9. Therefore, the product will be on back order during the interval where x is less than -9 or where x is greater than 25.
So, the product will be on back order from x = -∞ to x = -9 and from x = 25 to x = ∞.
x^2 - 16x - 225 < 0
Now, we need to solve for x by factoring the quadratic:
(x - 25)(x + 9) < 0
From this, we can see that the solutions are x = 25 and x = -9. Therefore, the product will be on back order during the interval where x is less than -9 or where x is greater than 25.
So, the product will be on back order from x = -∞ to x = -9 and from x = 25 to x = ∞.