1 The constraints of a linear programming problem are represented by the graph below. The feasible region is the unshaded region, including its boundaries.
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1. Write down the inequalities that define the feasible region. The objective is to maximise \(P _ { m } = x + m y\), where \(m\) is a positive, real-valued constant.
2. In the case when \(m = 2\), calculate the values of \(x\) and \(y\) at the optimal point, and the corresponding value of \(P _ { 2 }\).
3. (a) Write down the values of \(m\) for which point \(A\) is optimal.
   (b) Write down the values of \(m\) for which point \(B\) is optimal.