Max $2$X$1+4$X$2$

$(2/4)$X$1+(1/4)$X$2<40($#$1$ constraint$)$

$1$X$1+(10/9)$ X$2<100($#$2$ constraint$)$

$1$X$1+2\mathrm{.}5$X$2<200($#$3$ constraint$)$

$$X$1$ and X$2>0$

$11).$ Please use graphical method to find the FEASIBLE REGION. Please LABEL the $3$ constraints in your graph and indicate all the points you used.

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$2).$ Please draw an objective function line $($must write the equation here$)$ in the graph of $1)$ Mark the optimal solution as a star.

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$3).$ Please list the system of two equations $($crossing at the optimal solution point$)$

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$4).$ Please get the optimal solution of $3)$ with details: How much are X$1$ and X$2?$ You need to indicate the maximized output of the objective function.

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$2.$ Please answer the following questions $($list your answers on 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. $$

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$2).$ 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$).$

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

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

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$5).$ Will the optimal solution change if the coefficient of X$1$ in the objective function was changed to $3?$ Why?

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$6).$ Will the optimal solution change if the coefficient of X$2$ in the objective function was changed to $6?$ Why?

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

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

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$9).$ If the RHS of #$2$ constraint was changed to $101,$ how much will the new objective function output be$?$ Which cell did you refer to on the spreadsheet?

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