Question

40.0 Reyna runs a textile company that manufactures T-shirts. The profit, p, made by the company is modeled by the function p=s2+95-142, 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?

Answer 1

`\begin{gathered} p=s^2+9s-142 \\ \text{ Substiyute }p\text{ = 2000 into the equation above} \end{gathered}`
`\begin{gathered} 2000=s^2+9s-142 \\ 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+51)(s-42)=0 \\ s+51=0\text{ or s-42=0} \\ s=-51\text{ or s = 42} \end{gathered}`

But cannot be negative, hence s= 42. This implies that 42 shirts will be sold to make a profit of exactly $2000.

To earn a profit of more than $2000, then s must be greater than 42

This makes the answer to be s > 42

The correct answer is the second option