$1.$Given the following function for a LP model:Maximize Profit $($$$)$: Z $=8$X $+15$Y$.$Assume that the optimal solution is X $=4,$ Y $=2,$ which makes Z $=$ $$62.$If the objective coefficient for X is changed to $7.$ Assume that this does not affect the solution, what is the impact on the objective value?Question $5$ options:It will decrease by $$4$It will decrease by $$9$it will decrease by $$28$The solution remains the same, so there will be no change. it will increase by $$28$More information is required to answer this question it will increase by $$9$It will increase by $$4$

Q$2$ Assume that you have the following constraint as a part of LP model : X$+$ Y $<=50$

If the RHS of this constraint is changed to $54.$Assume that the shadow price is $1.$ What is the impact on objective value?

Options$-$ More info is required to solved this question

Objective value will increase by $27.$

Objective value will increase by $54.$

Objective value will decrease by $4.$

Objective value will decrease by $54.$

Objective value will decrease by $27.$

Objective value will increase by $4.$