MAX: $4x_1+4x_2$

Subject $to$: $2x_1+4x_{2}20$

$3x_1+5x_{2}15$

$x_1,x_{2}0$

decrease, enter $.)$

The objective function coefficient for variable $x_1$ can decrease by

or increase by

without changing the optimal solution.

$($b$)$ Is the optimal solution to this problem unique, or are there alternate optimal solutions?

Some of the allowable increase or decrease values for the RHS values are zero, so there are alternate optimal solutions.

None of the allowable increase or decrease values for the objective coefficients are zero, so the optimal solution is unique.

None of the allowable increase or decrease values for the RHS values are zero, so the optimal solution is unique.

Some of the allowable increase or decrease values for the objective coefficients are zero, so there are alternate optimal solutions.

We cannot determine if the optimal solution is unique based on our sensitivity report because the solution is degenerate.

$($d$)$ What is the optimal objective function value if $x_2$ equals $1?($Round your answer to three decimal places.$)$

$($e$)$ What is the optimal objective function value if the RHS value for the second constraint changes from $15$ to $22?($Round your answer to three decimal places.$)$