$2.$ Please answer the following questions $($please have your answers in this sheet$)$ based on the sensitivity analysis sheet from Solver.

$---$Tips: On the spreadsheet, Highlight the cells of coefficients, go to Tab Home group of "Cells", click button of "format", select "Format cells", then "number", then "fraction" up to two digits.

$1).$ What is the optimal solution? Must indicate the cells on the Spreadsheet where you find the answer.

$256\mathrm{.}36$

$2).$ How much are the ranges of optimality for the coefficients of X$1$ and X$2?($Must indicate the Cells you referred to on the spreadsheet$).$

$3).$ how much is the dual value for each constraint? $($Must indicate the Cells you referred to on the spreadsheet$).$

$4).$ Which constraints are binding? Why? $($must indicate what cells on the spreadsheet you used$)$

$5).$ Will the optimal solution change if the coefficient of X$1$ in the objective function was changed to $9?$ Why?

$6).$ Will the optimal solution change if the coefficient of X$2$ in the objective function was changed to $4\mathrm{.}5?$ Why?

$7).$ If the RHS of #$3$ constraint changed to $201,$ how much will the objective function output be increased? Which cell you referred to on the spreadsheet?

$8).$ If the RHS of #$1$ constraint changed to $41,$ how much will the objective function output be increased? Which cell you referred to on the spreadsheet?