The binding constraints for this problem are the second and third constraints are binding.

Min $x_1+2x_2$

$s.t.$

$x_1+x_2,300$

$2x_1+x_2,400$

$2x_1+5x_2,750$

$x_1,x_2,0$

$($a$)$ Keeping the second objective function coefficient fixed at $2,$ over what range can the first objective function coefficient vary before there is a change in the optimal solution point?

The first objective coefficient can from a low of to a high of

$($b$)$ Keeping the first objective function coefficient fixed at $1,$ over what range can the second objective function coefficient vary before there is a change in the optimal solution point?

The second objective coefficient can from a low of to a high of

$($c$)$ If the objective function becomes Min $1\mathrm{.}5x_1+2x_2,$ what will be the optimal values of $x_1$ and $x_2?$

$x_1=$

$x_2=(No$ Response$)$

What is the value of the objective function at the minimum?

$($d$)$ If the objective function becomes Min $7x_1+6x_2,$ what constraints will be binding? $($Select all that apply.$)$

First Constraint

Second Constraint

Third Constraint

$($e$)$ What is the dual value for the first constraint in the original problem?

What is the dual value for the second constraint in the original problem?

What is the dual value for the third constraint in the original problem?