Consider the following linear programming model and the accompanying sensitivity report.

MAX: $7$ X$1+4$ X$2$

Subject to: $2$ X$1+$ X$2<=16$

X$1+$ X$2<=10$

$2$ X$1+5$ X$2<=40$

X$1,$ X$2>=0$

Variable Cells

Cell Name

Final

Value

Reduced

Cost

Objective

Coefficient

Allowable

Increase

Allowable

Decrease

$B$$4$ Number to make: X$160713$

$C$$4$ Number to make: X$240430\mathrm{.}5$

Constraints

Final Shadow Constraint Allowable Allowable

Cell Name Value Price R$.$H$.$ Side Increase Decrease

$D$$8$ First constraint $1631642\mathrm{.}67$

$D$$9$ Second constraint $1011012$

$D$$10$ Third constraint $320401$E$+308$

Answer questions $13$ to $16$ based on Exhibit $2.$

$13.$ If there are simultaneous changes in the objective function coefficients of both decision variables

and that the coefficient of X$1$ changes to $5,$ then what is the maximum increase that the coefficient

of X$2$ can have so as to guarantee that there will be no change in the optimal solution?

A$.1$ C$.3$

B$.2$ D$.$ cannot be determined