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:

$\backslash$table$[[,$RHS$,$Allowable,Allowable,$],[$Constraint$,$Value,Increase,Decrease$],[1,10\mathrm{.}00000,1\mathrm{.}20000,2\mathrm{.}00000],[2,24\mathrm{.}00000,6\mathrm{.}00000,6\mathrm{.}00000],[3,16\mathrm{.}00000,$Infinite,$3\mathrm{.}00000]]$

What does the right$-$hand$-$side range information for constraint $1$ tell you about the dual value for constraint $1?$

The right$-$hand$-$side range for constraint $1$ is to $.$ As long as the right$-$hand side stays within this range, the dual valu

d$.$ The dual value for constraint $2$ is $0\mathrm{.}5.$ Using this dual value and the right$-$hand$-$side range information in part $($c$),$ what conclusion can be drawn about the effect of changes to the right$-$hand side of constraint $2?$ If required, 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 a right$-$hand side is between and

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