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 #s# is the number of T-shirts sold. How many T-shirts should be sold to earn a profit of more than $2,000?

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Answer 1 · 2016-04-05T19:29:29

#=> s>42#

Given condition requires #p>$2000#

But #p=s^2+9s-142#

#=> s^2+9s-142>$2000#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine the point where p=$2000")#

#=>s^2+9s-142=2000#

#=>s^2+9s-2142=0#

#=>(s+9/2)^2-2142-(9/2)^2=0#

#=>(s+9/2)^2=2142+(9/2)^2#

#=>(s+9/2)^2=8649/4#

taking the square root of both sides

#=>s+9/2=93/2#

#=>s=42#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~
So if 42 tee shirts give the $2000 we need more than that profit so we need more that 42 tee shirts.

#=> s>42#