$.$ Determine the optimal solution and the optimal objective function value.

b$.$ Find the range of values of the right hand side of constraint $2$ for which the current basis

remains optimal. How do the optimal decision variables and optimal objective function values

change if the right hand side of constraint $2$ increases by $5?$ How do these values change if the

right hand side of constraint $2$ decreases by $3?$

c$.$ Find the range of values of the objective function coefficient of $3$ for which the current basis

remains optimal.

d$.$ Find the range of values of the objective function coefficient of $1$ for which the current basis

remains optimal. How do the optimal decision variables and optimal objective function values

change if the objective function coefficient of $1$ changes to $14?$