Consider the following linear program:

Max $3$A $+2$B

s$.$t$.$

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

$3$A $+1$B $<=26$

$1$A $+2$B $<=20$

$$ A$,$B $>=0$

The value of the optimal solution is $28.$Suppose that the right$-$hand side of the constraint $1$is increased from $10$to $11.$

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: fill in the blank $2$

The computer solution for the linear program in Problem $1$provides the following right$-$hand$-$side range information:

$$

Constraint RHS Value Allowable Increase Allowable Decrease

$110\mathrm{.}000003\mathrm{.}200001\mathrm{.}33333$

$226\mathrm{.}000004\mathrm{.}0000016\mathrm{.}00000$

$320\mathrm{.}00000$ Infinite $8\mathrm{.}00000$

A$.$ What does the right$-$hand$-$side range information for constraint $1$tell you about the dual value for constraint $1?$If required, round your answers to five decimal places.

The right$-$hand$-$side range for constraint $1$is fill in the blank $3$to fill in the blank $4.$As long as the right$-$hand side stays within this range, the dual value

$.$

B$.$ 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.

C$.$ The improvement in the value of the optimal solution will be fill in the blank $6$for every unit increase in the right$-$hand side of constraint $2$as long as the right$-$hand side is between fill in the blank $7$and fill in the blank $8.$