Consider the following linear program

$($

LP

$)$

:

min

x

$,$

y

$3$

x

$+$

$2$

y

$($

$1$

a

$)$

s

$.$

t

$.$

$2$

x

$+$

$3$

y

$>$

$=$

$1$

$2$

$($

$1$

b

$)$

$$

$2$

x

$+$

$3$

y

$<$

$=$

$6$

$($

$1$

c

$)$

x

$>$

$=$

$2$

$($

$1$

d

$)$

x

$,$

$$y

$>$

$=$

$0$

$($

$1$

e

$)$

$($

a

$)$

$[$

$3$

$]$

$$Plot the feasible region

$($

by hand

$)$

$.$

$$Is the feasible region bounded? What are the feasible

corner points?

$($

b

$)$

$[$

$3$

$]$

$$Solve the LP from your plot. What are the optimal solution and the optimal value? Is the

LP bounded?

$[$

$6$

$]$

$$Consider the following linear program

$($

LP

$)$

:

$$

$$

$$

$$

$,$

$$

$3$

$$

$+$

$2$

$$

$$

$$

$.$

$$

$.$

$2$

$$

$+$

$3$

$$

$>=$

$1$

$2$

$-$

$2$

$$

$+$

$3$

$$

$<=$

$6$

$$

$>=$

$2$

$$

$,$

$$

$>=$

$0$