$5.$ True$-$False questions. Provide a reason for your answer.a$)$ There is a unique optimal solution to a linear optimization provide. A new constraint is now added. Is it possible the previous solution remains optimal. T or F$.$b$)$ For a maximization problem, the quantity of basic variables must naturally be greater than the number of constraints to obtain better solutions. T or Fc$)$ Dictionary method is preferable to the Tableau method because there are fewer mathematical operations required.d$)$ The constraint limit for a constraint' in maximization problem is increased. Theoptimal objective function will always improve. T or F$.$e$)$ If there are alternative optimal solutions to a linear problem, there can be more than $2$ solutions with the same objective function? T or F$.$f Every basic solution is associated with an extreme point of the feasible region? T or F g$)$ This an example of a linear constraint: $-$x$2+4$x$3(3+$ x$4)+3$xs $8,$ specifically why or why not?h$)$ x$2$ is a non$-$basic variable in the optimal solution for a maximization problem and the objective function coefficient for x$2$ is c$2.$ If c$2$ is decreased, x$2$ will never become a basic variable. T or F$.$i$)$ At the final iteration of the simplex algorithm for a maximization problem using tableaus, the minimum coefficient is zero for a non$-$basic variable in row $0.$ For this problem, there will definitely be a unique optimal solution.j$)$ Two solutions on an iso$-$profit line can have different objective function values depending on how close they are to the optimal solution. T or F$.$