Reyna runs a textile company that manufactures t-shirts. the profit, p, made by the company is modeled by the function mc025-1.jpg, where s is the number of t-shirts sold. how many t-shirts should be sold to earn a profit of more than $2,000?

Plug in 2000 into the equation as an inequality, 2000> s^2 + 9s -142. now solve for s, 0> s^2 + 9s -2142 which gives you 0> (s+51)(s-42)
then you get 42> s : )

answer:

s > 42

step-by-step explanation:

1) write the inequality using the information given.

s^2 + 9s - 142 > 2000 the profit (modeled by s^2 + 9s - 142 ) should be greater than $2000.

2) solve the inequality to find the critical points.

s^2 + 9s - 142 > 2000 s^2 + 9s - 142 - 2000 > 0 s^2 + 9s - 2142 > 0 s^2 + 51s - 42s -2142 > 0 s (s + 51) - 42 (s + 51) > 0 (s - 42)(s + 51) > 0 s = 42 and s = -51

3) set up the number line and determine the intervals.

-51 42there are three intervals: s < -51 -51 < s < 42 s > 42

4) test a number from each interval to see which one makes the original statement (s^2 + 9s - 142 > 2000) true.

the only one that works is s > 42, therefore that is the answer.