$1.(20$ pts$)$ The following graph depicts the optimal value of a linear program, denoted by z $,$ as the right$-$hand side of one of the constraints, denoted by RHS$,$ changes. $($a$)$ Determine whether this LP is a maximization or minimization problem, and whether the constraintis a or a constraint. Explain your reasons. $($b$)$ Now replace RHS by objective coefficient and interpret this graph depicting how the optimal objective changes as the objective coefficient of a primal variable is changed. Determine if the linear program is a maximization or minimization problem, and whether the $($optimal$)$ value of the primal variable is nonnegative or nonpositive.