Suppose that the objective function to be maximized is the piecewise linear function: [ f= begin{cases}2 x_{1}+x_{2}

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Suppose that the objective function to be maximized is the piecewise linear function:

\[ f= \begin{cases}2 x_{1}+x_{2} & \text { if } x_{1} \leq 1 / 2 \\ x_{1}+x_{2}+1 / 2 & \text { otherwise }\end{cases} \]

Sketch the \(c\)-level sets carefully in order to maximize \(f\) over the feasible region of Exercise 8.

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