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Consider the following optimization problem
$\max (2 x+3 y)$
subject to the following three constraints
\begin{aligned} x+y & \leq 5, \\ x+2 y & \leq 10, \text { and } \\ x & <3 . \end{aligned}
Let $z^{*}$ be the smallest number such that $2 x+3 y \leq z^{*}$ for all $(x, y)$ which satisfy the above three constraints. Which of the following is true?

1. There is no $(x, y)$ that satisfies the above three constraints.
2. All $(x, y)$ that satisfy the above three constraints have $2 x+3 y$ strictly less than $z^{*}$.
3. There are exactly two $(x, y)$ that satisfy the above three constraints such that $2 x+3 y$ equals $z^{*}$.
4. There is a unique $(x, y)$ that satisfies the above three constraints such that $2 x+3 y$ equals $z^{*} \cdot$
5. There are infinitely many $(x, y)$ that satisfy the above three constraints such that $2 x+3 y$ equals $z^{*}$.