in Others edited by
7 views
1 vote
1 vote

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 $z^{*}$.
in Others edited by
by
41.3k points
7 views

Please log in or register to answer this question.

Welcome to GO Electronics, where you can ask questions and receive answers from other members of the community.