Problem

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° larger than angle X
• Angle Y must be at most 120°

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.