Graph $($i$)$

b$.$ Use the solution to part $($a$)$ to determine the dual value for constraint $1.$ If required, round your answer to $1$ decimal place.

Dual Value:

c$.$ The computer solution for the linear program in Problem $1$ provides the following right$-$hand$-$side range information:

What does the right$-$hand$-$side range information for constraint $1$ tell you about the dual value for constraint $1?$ If required, round your answers to five decimal places.

The right$-$hand$-$side range for constraint $1$ is

to

$.$ As long as the right$-$hand side stays within this range, the dual value

round your answers to $1$ decimal place.

The improvement in the value of the optimal solution will be

$$ for every unit increase in the right$-$hand side of constraint $2$ as long as the right$-$hand side is between

$x$ and

$x.$