D,I 12.6-1.* Use the BIP branch-and-bound algorithm presented in Sec. 12.6 to solve the following problem interactively.
\[
\text { Maximize } \quad Z=2 x_{1}-x_{2}+5 x_{3}-3 x_{4}+4 x_{5}
\]
subject to
\[
\begin{array}{r}
3 x_{1}-2 x_{2}+7 x_{3}-5 x_{4}+4 x_{5} \leq 6 \\
x_{1}-x_{2}+2 x_{3}-4 x_{4}+2 x_{5} \leq 0
\end{array}
\]
and
\[
x_{j} \text { is binary, } \quad \text { for } j=1,2, \ldots, 5 .
\]
D.I 12.6-2. Use the BIP branch-and-bound algorithm presented in Sec. 12.6 to solve the following problem interactively.
\[
\text { Minimize } \quad Z=5 x_{1}+6 x_{2}+7 x_{3}+8 x_{4}+9 x_{5}
\]
subject to
\[
\begin{aligned}
3 x_{1}-x_{2}+x_{3}+x_{4}-2 x_{5} & \geq 2 \\
x_{1}+3 x_{2}-x_{3}-2 x_{4}+x_{5} & \geq 0 \\
-x_{1}-x_{2}+3 x_{3}+x_{4}+x_{5} & \geq 1
\end{aligned}
\]
and
\( x_{j} \) is binary, \( \quad \) for \( j=1,2, \ldots, 5 \).
D,I 12.6-3. Use the BIP branch-and-bound algorithm presented in Sec. 12.6 to solve the following problem interactively.
\[
\text { Maximize } \quad Z=5 x_{1}+5 x_{2}+8 x_{3}-2 x_{4}-4 x_{5},
\]
subject to
\[
\begin{aligned}
-3 x_{1}+6 x_{2}-7 x_{3}+9 x_{4}+9 x_{5} & \geq 10 \\
x_{1}+2 x_{2}-x_{4}-3 x_{5} & \leq 0
\end{aligned}
\]
and
\( x_{j} \) is binary, \( \quad \) for \( j=1,2, \ldots, 5 \).
D,I 12.6-4. Reconsider Prob. 12.3-6(a). Use the BIP branch-andbound algorithm presented in Sec. 12.6 to solve this BIP model interactively.
D,I 12.6-5. Reconsider Prob. 12.4-10(a). Use the BIP algorithm presented in Sec. 12.6 to solve this problem interactively.