Implement the following LP model in a spreadsheet. Use Solver to solve the problem and create a Sensitivity Report. Use this information to answer the following questions:

MIN: $5x_1+3x_2+4x_3$

Subject $to$: $x_1+x_2+2x_{3}2$

$5x_1+3x_2+2x_{3}1$

$x_1,x_2,x_{3}0$

a$.$ What is the smallest value the objective function coefficient for $x_3$ can assume without changing the optimal solution?

b$.$ What is the optimal objective function value if the objective function coefficient for $x_3$ changes to $-1?($Hint: The answer to this question is not given in the Sensitivity Report. Consider what the new objective function is relative to the constraints.$)$