Carefully examine a sample QM output below. Answer the questions that follow using the information provided in the table.

Linear Programming

Results

Maximize

Const $1$

Const $2$

Const $3$

Solution

Ranging

X$1$

X$2$ X$3$ RHS Dual

$152016$

$5$

$64<=2100$

$108$

$5<=2002\mathrm{.}27$

$42$

$5<=1700\mathrm{.}93$

$5$

$32612$

Variable Value Reduced Original Value Lower Bound Upper Bound

X$1$

$11\mathrm{.}4$

$15$

$-$ Infinity

$26\mathrm{.}4$

X$2$

$5$

$20$

$25\mathrm{.}6$

X$3$

$32$

$16$

$12\mathrm{.}5$

$50$

CONSTRAINT

Dual value

Slack$/$Surplus

Original

Value

Lower

Bound

Upper

Bound

Constraint $1$

$0$

$52$

$210$

$158$

infinity

Constraint $2$

$2\mathrm{.}27$

$200$

$170$

$270\mathrm{.}91$

Constraint $3$

$0\mathrm{.}933$

$170$

$50$

$200$

If the profit from X$2$ increases to $$24,$ what happens to the optimal solution?

$$The profit remains the same.

$$The corner point remains the same; however, the profit would reduce by $$20.$

$$The corner points changes but the profit remains the same.

$$The corner point remains the same; however, new profit would be $$632.$

$$None of the above is correct.