Consider the linear program in Problem $3.$ The value of the optimal solution is $48.$ Suppose that the right$-$hand side for constraint $1$ is increased from $9$ to $10.$

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 $3$ provides the following righthand$-$side range information:

$\backslash$table$[[$Constraint$,\backslash$table$[[$RHS$],[$Value$]],\backslash$table$[[$Allowable$],[$Increase$]],\backslash$table$[[$Allowable$],[$Decrease$]]],[1,9\mathrm{.}00000,2\mathrm{.}00000,4\mathrm{.}00000],[2,10\mathrm{.}00000,8\mathrm{.}00000,1\mathrm{.}00000],[3,18\mathrm{.}00000,4\mathrm{.}00000,$Infinite$]]$

What does the right$-$hand$-$side range information for constraint $1$ tell you about the dual value for constraint $1?$

d$.$ The dual value for constraint $2$ is $3.$ Using this dual value and the right$-$hand$-$side range information in part $($c$),$ what conclusion can be drawn about the effect of changes to the right$-$hand side of constraint $2?$