Consider the linear program shown in $29\mathrm{.}1-1.($a$)$ Give an optimal solution and its optimal value. $($b$)$ Show its dual program and the corresponding dual optimal solution.

Consider the linear program

Minimize $-2$x$1+3$x$2$

Subject to

x$1+$ x$2=7$

x$1-2$x$24$

x$10$

Give three feasible solutions to this linear program. What is the objective value of each one?