Consider the following linear programming problem:

Minimize $2$A $+4$B $=$ Z

Constraints:

$4$A $+6$B $>=120$

$2$A $+6$B $>=72$

B $>=10$

A$,$ B $>=0$

If after we solved it with solver, we found the optimal solution is A $=15$ and B $=10,$ and the objective value Z $=70.$ The shadow price for the third constraint $($i$.$e$.$ B $>=10)$ is $2.$ The allowable increase and the allowable decrease are $10$ and $6,$ respectively. Based on the statements above, which of the following is correct?

Group of answer choices

none of the above

If you decrease the right$-$hand value of the third constraint to $2,$ the optimal Z will be equal to $62.$

If you increase the right$-$hand value of the third constraint to $15,$ the optimal Z will be equal to $75.$

If you decrease the right$-$hand value of the third constraint to $9,$ the optimal Z will stay the same.

If you increase the right$-$hand value of the third constraint to $15,$ the optimal Z will be equal to $80.$