Question

Reyna runs a textile company that manufactures T-shirts. The profit, p, made by the company is modeled by the function , 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?
a) s < 42
b) s > 42
c) s > 51
d) s < 51

Answer 1

Answer:

s > 42

Step-by-step explanation: INCOMPLETE QUESTION, PROBLEM STATEMENT DOES NOT GIVE THE MODELING FUNCTION.

I´VE FOUND IN NTERNET   PROFIT

p(s) = s² + 9*s - 142

Then we have

s² + 9*s - 142 > 2000

rearrange that inequation

s² + 9*s  - 142 > 2000      ⇒  s² + 9*s  - 2142  >  0

we complete the expression as a perfect quadratic, with the help of two number that add +9  and multiplying  - 2142

Numbers are  51 and  - 42    

then

factoring that expression as a perfect quadratic

( s + 51 )* ( s - 42 ) > 0

For what  have two solution, and we dismiss the negative value since the numbers of shirts could not be negative, we get

s - 42 > 0

s > 42  the solution