Answer:
The number of key rings sold on a particular day when the total profit is $5,000 is 4,000 rings.
Step-by-step explanation:
The question is incomplete.
<em>An owner of a key rings manufacturing company found that the profit earned (in thousands of dollars) per day by selling n number of key rings is given by </em>
<em />
<em />
<em>where n is the number of key rings in thousands.</em>
<em>Find the number of key rings sold on a particular day when the total profit is $5,000.</em>
<em />
We have the profit defined by a quadratic function.
We have to calculate n, for which the profit is $5,000.
![P=n^2-2n-3=5\\\\n^2-2n-8=0](https://tex.z-dn.net/?f=P%3Dn%5E2-2n-3%3D5%5C%5C%5C%5Cn%5E2-2n-8%3D0)
We have to calculate the roots of the polynomial we use the quadratic equation:
![n=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\n= \frac{-2\pm\sqrt{4-4*1*(-8)}}{2}= \frac{-2\pm\sqrt{4-32}}{2} = \frac{-2\pm\sqrt{36}}{2} =\frac{-2\pm6}{2} \\\\n_1=(-2-6)/2=-8/2=-4\\\\n_2=(-2+6)/2=4/2=2](https://tex.z-dn.net/?f=n%3D%5Cfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%5C%5C%5C%5Cn%3D%20%5Cfrac%7B-2%5Cpm%5Csqrt%7B4-4%2A1%2A%28-8%29%7D%7D%7B2%7D%3D%20%5Cfrac%7B-2%5Cpm%5Csqrt%7B4-32%7D%7D%7B2%7D%20%3D%20%5Cfrac%7B-2%5Cpm%5Csqrt%7B36%7D%7D%7B2%7D%20%3D%5Cfrac%7B-2%5Cpm6%7D%7B2%7D%20%5C%5C%5C%5Cn_1%3D%28-2-6%29%2F2%3D-8%2F2%3D-4%5C%5C%5C%5Cn_2%3D%28-2%2B6%29%2F2%3D4%2F2%3D2)
n1 is not valid, as the amount of rings sold can not be negative.
Then, the solution is n=4 or 4,000 rings sold.