This output describes a two variable linear program, solved in Excel to optimality. The output shown

below is the final output, after the problem has been fully solved. The problem has $2$ variables, three

$($non$-$trivial$)$ constraints and two non$-$negativity constraints. The second part of the output describes

the sensitivity analysis for this problem. The objective is of a MAXIMIZATION type $(=$MAX $7$X$1+10$X$2).$ HINT: Please watch the sensitivity report carefully. USE THE CONSTRAINT RIGHT HAND SIDES AND THE

OBJECTIVE COEFFICIENT VALUES TO MAP THE DUAL VARIABLES TO THE CONSTRAINTS. For instance,

the dual variable value $($shadow price$)$ of $7$ corresponds to the constraint with a Right hand side $($RHS$)$ of

$40.$ Make a note of this as you answer the problems. So $J$$8$ is X$1<=50$; $J$$9$ is X$2<=60$; and $J$$10$ is

X$1+2$X$2<=40$ Which of the following statements is true?

If the objective function coefficient for X$1$ is changed from $7$X$1$ to $6$X$1,$ the new optimal solution value is $240.$

If the objective function coefficient for X$2$ is changed from $10$X$2$ to $15$X$2,$ the optimal corner point remains the same at $(40,0).$

If the objective function coefficient for X$1$ is changed from $7$X$1$ to $6$X$1,$ the new optimal solution value is $200$ because the best corner point does not change for this level of change.

The objective coefficient for X$2$ can be increased without bound and the optimal corner point will always stay the same.