Refer to the following sensitivity report:

Variable cells

CellNameFinal ValueReduced CostObjective CoefficientAllowable IncreaseAllowable Decrease$B$$2$Product$\_102521$E$+30$$B$$3$Product$\_2175071$E$+301$$B$$4$Product$\_301\mathrm{.}591\mathrm{.}51$E$+30$

Constraints

CellNameFinal ValueShadow PriceConstraint R$.$H$.$ SideAllowable IncreaseAllowable Decrease$H$$9$Resource A$001001$E$+30100$$H$$10$Resource B$52508001$E$+30275$$H$$11$Resource C$7001\mathrm{.}75700366\mathrm{.}6666667700$

If the objective function coefficient for Product$\_1$ were increased to a value of $8,$ which of the following would be TRUE?

The optimal solution would change.

The optimal objective function value would stay the same.

Product$\_1$ would enter the solution $($the final value of the variable Product$\_1$ would be greater than zero$).$

Multiple Choice

I only

II only

III only

I, II$,$ and III are all true.

Only I and III are true.