reyna runs a textile company that manufactures t - shirts. the profit, p, made by the company is modeled by…

Explanation:

Step1: Set up the inequality

We want $p>2000$, so $s^{2}+9s - 142>2000$. Rearranging gives $s^{2}+9s-2142 > 0$.

Step2: Solve the quadratic - equation

For the quadratic equation $s^{2}+9s - 2142=0$, where $a = 1$, $b = 9$, and $c=-2142$. The quadratic formula is $s=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. First, calculate the discriminant $\Delta=b^{2}-4ac=(9)^{2}-4\times1\times(-2142)=81 + 8568=8649$. Then $s=\frac{-9\pm\sqrt{8649}}{2}=\frac{-9\pm93}{2}$. We get two solutions: $s_1=\frac{-9 + 93}{2}=\frac{84}{2}=42$ and $s_2=\frac{-9 - 93}{2}=\frac{-102}{2}=-51$.

Step3: Determine the solution of the inequality

Since the quadratic function $y = s^{2}+9s - 2142$ is a parabola opening upwards (because $a = 1>0$), the solution of the inequality $s^{2}+9s - 2142>0$ is $s>42$ or $s < - 51$. But the number of T - shirts sold $s$ cannot be negative. So the solution is $s>42$.

Answer:

B. $s>42$