$1.$ What is the optimal solution including the optimal value of the objective function? $(5$pts$)$

$2.$ Suppose the unit cost of A is decreased to $$4.$ Is the current solution still optimal? What is the value of the objective function when this unit cost is decreased to $$4?(4$pts$)$

$3.$ How much can the unit cost of B be decreased without concern for the optimal solution changing? $(4$pts$)$

$4.$ If simultaneously the cost of x$$ was raised to $$7\mathrm{.}5$ and the cost of x$2$ was reduced to $$6,$ would the current solution remain optimal? What will be the optimal cost? $(4$pts$)$

$5.$ What is the maximum amount the company should pay for $20$ extra units of resources $27(4$pts$)$

$6.$ What is the maximum amount the company should pay for $2$ extra pounds of material $17(4$pts$)$

$7.$ If the right$-$hand side of constraint $3$ is increased by $1,$ what will be the effect on the optimal solution? Explain the changes if there's any. $($Aside from the Z$-$value$).(5$pts$)$

$8.$ What is the impact of deleting the second constraint on the optimal solution? Why? $(5$pts$)$

$9.$ What is the impact of deleting the first constraint on the optimal solution? Why? $(5$pts$)$