Consider the following linear program.Max$3$A$+2$Bs$.$t$\mathrm{.}1$A$+1$B$<=103$A$+1$B$<=261$A$+2$B$<=16$A$,$B$>=0$

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What is the value of the objective function at the optimal

solution?

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$\_\_\_\_\_\_\_$ at $($A$,$ B$)=(\_\_\_\_\_\_\_\_)$Does the optimal solution change? The

extreme point $(\_\_\_\_\_)$ remains or becomes optimal. Th 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.$$d$.$ The extreme

point $(\_\_\_\_\_)$ remains or becomes optimal. The value of the

objective function becomes $\_\_\_\_\_$e$.$ The computer

solution for the linear program in part $($a$)$ provides the following

objective coefficient range information.VariableObjective

CoefficientAllowable

IncreaseAllowable

DecreaseA$3\mathrm{.}000003\mathrm{.}000001\mathrm{.}00000$B$2\mathrm{.}000001\mathrm{.}000001\mathrm{.}00000$Use this objective coefficient range

information to answer parts $($b$)$ and $($c$).$The objective coefficient for variable A is $\_\_\_\_\_$ to $\_\_\_\_\_.$

Since the change in part $($b$)$ is within or

outside this range, we know the optimal solution

will or will not change. The objective

coefficient range for variable B is $\_\_\_\_\_$ to $\_\_\_\_\_.$ Since the

change in part $($c$)$ is $\_\_\_\_\_$ this range, we know the optimal

solution will or will not change.