2. Chris has been asked to design a badge in the shape of a triangle XYZ subject to the following constraints.

\begin{itemize}
  \item Angle $Y$ should be at least three times the size of angle $X$
  \item Angle $Z$ should be at least $50 ^ { \circ }$ larger than angle $X$
  \item Angle $Y$ must be at most $120 ^ { \circ }$
\end{itemize}

Chris has been asked to maximise the sum of the angles $X$ and $Y$.\\
Let $x$ be the size of angle $X$ in degrees.\\
Let $y$ be the size of angle $Y$ in degrees.\\
Let z be the size of angle $Z$ in degrees.\\
Formulate this information as a linear programming problem in $x$ and $y$ only. State the objective and list the constraints as simplified inequalities with integer coefficients.

You are not required to solve this problem.\\

\hfill \mbox{\textit{Edexcel D1 2021 Q2 [6]}}