Consider the following linear program. Max $3$A $+2$B s$.$t$.1$A $+1$B $<=103$A $+1$B $<=221$A $+2$B $<=18$ A$,$ B $>=0($A$)$Use the graphical solution procedure to find the optimal solution. What is the value of the objective function at the optimal solution? $\_\_\_\_\_\_\_\_\_\_\_\_$ at $($A$,$ B$)=\_\_\_\_\_\_\_\_\_\_\_\_($b$)$ Assume that the objective function coefficient for A changes from $3$ to $5.$ Use the graphical solution procedure to find the new optimal solution. Does the optimal solution change? The extreme point $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_---$Select$---$remainsbecomes optimal. The value of the objective function becomes $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_($c$)$ Assume that the objective function coefficient for A remains $3,$ but the objective function coefficient for B changes from $2$ to $4.$ Use the graphical solution procedure to find the new optimal solution. Does the optimal solution change? The extreme point $\_\_\_\_\_\_\_\_\_\_\_\_---$Select$---$remainsbecomes optimal. The value of the objective function becomes $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$