Consider the following linear program:

Max $3$A$+2$B

s$.$t

$1$A$+1$B$<=10$

$3$A$+1$B$<=24$

$1$A$+2$B$<=16$

A$,$ B$>=0$

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

b$.$ Assume that the objective function coefficient for A changes from $3$ to $5.$ Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution.

c$.$ Assume that the objective function coefficient for A remains $3,$ but the objective function coefficient B changes from $2$ to $4.$ Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution.

d$.$ The sensitivity report for the linear program in part $($a$)$ provides the following objective coefficient range information:

Variable

Objective Coefficient

Allowable increase

Allowable decrease

A

$3\mathrm{.}000$

$3\mathrm{.}000$

$1\mathrm{.}000$

B

$2\mathrm{.}000$

$1\mathrm{.}000$

$1\mathrm{.}000$

Use this objective coefficient range information to answer parts b and c$.$