Question

Reyna runs a textile company that manufactures T-shirts. The profit, p, made by the company is modeled by the function p=s^2+9s-142 where is the number of T-shirts sold. How many T-shirts should be sold to earn a profit of more than $2,000?

Answer 1

`p = s \: 2 + 9s - 142`

Answer 2

Number of t shirts to be sold to have a profit of $2,000 = 42

Explanation:

We have profit

`p=s^2+9s-142`

We need to find how many T-shirts should be sold to earn a profit of more than $2,000, that is

`s^2+9s-142\geqslant 2000\\s^2+9s-2142\geqslant 0\\s=(-9\pm √(9^2-4* 1* (-2142))))/(2* 1)\\s=(-9\pm 93)/(2)\\s=42\texttt{ or }-51`

Number of t shirts to be sold to have a profit of $2,000 = 42