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

• Angle \(Y\) should be at least three times the size of angle \(X\)
• Angle \(Z\) should be at least \(50 ^ { \circ }\) larger than angle \(X\)
• Angle \(Y\) must be at most \(120 ^ { \circ }\)

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.