Excel's Solver has been used in the spreadsheet below to solve a linear programming problem with a maximization objective function. The two tables below show the input section and the sensitivity analysis, respectively.

Direction: For numerical answers, round non$-$integer values to $2$ decimal places. Keep integer values as integers.

What is the optimal value for $x_1?$

Answer: $x_1=$

What is the optimal value for $x_2?$

Answer: $x_2=$

Would you pay $$1\mathrm{.}30$ each for up to $50$ more units of resource $2?$

Answer: Enter Y'es or No$.$

Is the current solution still optimal even when the objective function coefficient of product $2$ is decreased to $2?$

Answer: $$ Enter Y'es or No$.$

Does the second constraint have a slack or a surplus? What is its current value?

Answers: $$

If $30$ units of resource $1$ were available, would the profit increase by $$5\mathrm{.}4?$

Answer $$ Enter Y'es or No$.$

Input Section:

$\backslash$table$[[,x_1,x_2,,,],[$Objective function Coefficients,$5,4,,,],[$Constraints$,,,$Constraint Sign,RHS$,],[$#$1,2,5,,40,],[$H$2,3,1,,30,],[$#$3,1,1,,12,]]$

Sensitivity Analysis:

$\backslash$table$[[$Variable$,$Final Value,Reduced Cost,Objective Coefficient,Allowable Increase,Allowable Decrease$],[x_1,8\mathrm{.}4615,0,5,7,3\mathrm{.}4],[x_2,4\mathrm{.}6154,0,4,8\mathrm{.}5,2\mathrm{.}3333]]$

$\backslash$table$[[$Constraint$,$Final Value,Dual Price,RHS Value,Allowable Increase,Allowable Decrease$],[$#$1$ LHS$,40,0\mathrm{.}5385,40,110,7],[$#$2$ LHS$,30,1\mathrm{.}3077,30,30,4\mathrm{.}6667],[$#$3$ LHS$,13\mathrm{.}0769,0,12,1\mathrm{.}0769,1E+30$