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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?

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