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

Answer:

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

Step-by-step 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

      $s^2+9s-142\geqslant 2000\\s^2+9s-2142\geqslant 0\\s=\frac{-9\pm \sqrt{9^2-4\times 1\times (-2142))}}{2\times 1}\\s=\frac{-9\pm 93}{2}\\s=42\texttt{ or }-51$

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