Use this objective coefficient range information to answer parts $($b$)$ and $($c$).$

$2.$ Consider the linear program in Problem $1.$ The value of the optimal solution is $27.$ Suppose that the right$-$hand side for constraint $1$ is increased from $10$ to $11.$

a$.$ Use the graphical solution procedure to find the new optimal solution.

b$.$ Use the solution to part $($a$)$ to determine the dual value for constraint $1.$

c$.$ The computer solution for the linear program in Problem $1$ provides the following right$-$hand$-$side range information:

$\backslash$table$[[$Constraint$,\backslash$table$[[$RHS$],[$Value$]],\backslash$table$[[$Allowable$],[$Increase$]],\backslash$table$[[$Allowable$],[$Decrease$]]],[1,10\mathrm{.}00000,1\mathrm{.}20000,2\mathrm{.}00000],[2,24\mathrm{.}00000,6\mathrm{.}00000,6\mathrm{.}00000],[3,16\mathrm{.}00000,$Infinite,$3\mathrm{.}00000]]$