To solve the exercise you know that the income from selling x units of the product must be greater than the cost of producing these units of the product, then
[tex]\begin{gathered} R(x)>C(x) \\ 150x>125x+800 \end{gathered}[/tex]Now, you can solve the inequality
[tex]\begin{gathered} 150x>125x+800 \\ \text{ Subtract 125x from both sides of the inequality} \\ 150x-125x>125x+800-125x \\ 25x>800 \\ \text{ Divide by 25 from both sides of the inequality} \\ \frac{25x}{25}>\frac{800}{25} \\ x>32 \end{gathered}[/tex]Therefore, for values of x greater than 32, this product will generate a profit.
