Graphical Solution and Range of Optimality for Objective Function Coefficients. Consider the linear program below and answer the following. LO $1,4$ Min s$.$t$.8$X$112$Y$1$X$13$Y$ $92$X$12$Y$ $106$X$12$Y$ $18$ A$,$ B $ $0$a$.$ Use the graphical solution procedure to find the optimal solution. b$.$ Assume that the objective function coefficient for X changes from $8$ to $6.$ Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution.$$c$.$ Assume that the objective function coefficient for X remains $8,$ but the objective function coefficient for Y changes from $12$ to $6.$ Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution.$$d$.$ The computer solution for the linear program in part $($a$)$ provides the following objective coefficient range information:$$Variable X$$Y$$Objective Coefficient$8\mathrm{.}0000012\mathrm{.}00000$Allowable Increase$4\mathrm{.}0000012\mathrm{.}00000$Allowable Decrease$4\mathrm{.}000004\mathrm{.}00000$How would this objective coefficient range information help you answer parts $($b$)$ and $($c$)$ prior to re$-$solving the problem?