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

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 $c_2$ fixed at $2,$ over what range can $c_1$ vary before there is a change in the optimal solution point?

b$.$ Keeping $c_1$ fixed at $1,$ over what range can $c_2$ vary before there is a change in the optimal solution point?

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

d$.$ If the objective function becomes Min $7x_1+6x_2,$ what constraints will be binding?

e$.$ Find the dual price for each constraint in the original problem.