$2.$ Consider the linear program in Problem $1.$ The value of the optimal solution is $27.$ Suppose that the right$-$hand side for constraint $1$ is increased from $10$ to $11.$

a$.$ Use the graphical solution procedure to find the new optimal solution.

b$.$ Use the solution to part $($a$)$ to determine the shadow price for constraint $1.$

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

Constraint

$1$

$2$

$3$

Constraint

R$.$H$.$ Side

$10\mathrm{.}000$

$24\mathrm{.}000$

$16\mathrm{.}000$

Allowable

Increase

$1\mathrm{.}200$

$6\mathrm{.}000$

Infinite

Allowable

Decrease

$2\mathrm{.}000$

$6$

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

d$.$ The shadow price for constraint $2$ is $0\mathrm{.}5.$ Using this shadow price and the right$-$hand$-$ side range information in part $($c$),$ what conclusion can you draw about the effect of changes to the right$-$hand side of constraint $2?$