Answer :
To answer this problem we have to remember that the break even point occur where the revenue function and the cost function have the same value.
Then, this happens when
[tex]C(x)=R(x)[/tex]Pluggin the expressions of our functions and solving for x we have:
[tex]\begin{gathered} 0.76x+77700=1.81x \\ 77700=1.81x-0.76x \\ 77700=1.05x \\ x=\frac{77700}{1.05} \\ x=74000 \end{gathered}[/tex]Therefore the break even point occurs when x=74000. In this points both functions have value
[tex]\begin{gathered} C(74000)=133940 \\ R(74000)=133940 \end{gathered}[/tex]