$500$

$350$

$550$

$500$

A

B

$1$

$2$

$$7$

$$2$

$$6$

$$5$

Supply

Demand

$[$Graphs generated by this script: initPicture$(-16,16,-6,10)$;circle$([-8,5],3)$; circle$([8,5],3)$; circle$([-8,-3],3)$; circle$([8,-3],3)$;text$([-14,5],"500")$; text$([14,5],"350")$; text$([-14,-3],"550")$; text$([14,-3],"500")$;text$([-8,5],"$A$")$; text$([-8,-3],"$B$")$; text$([8,5],"1")$; text$([8,-3],"2")$;fontsize$="13"$; text$([-2,5\mathrm{.}6],"$$$7")$; text$([-1\mathrm{.}5,3\mathrm{.}5],"$$$2")$; text$([-3,0],"$$$6")$;text$([-2,-2\mathrm{.}3],"$$$5")$;text$([-8,8],$"Supply"$)$;text$([8,8],$"Demand"$)$;marker$=$'arrow'; line$([-5,5],[5,5])$; marker$=$'arrow'; line$([-5,5],[5,-3])$; marker$=$'arrow'; line$([-5,-3],[5,5])$;marker$=$ 'arrow'; line$([-5,-3],[5,-3])$;$]$

Formulate an LP model for this transportation network above.

x

i

j

$=$ number of units shipped from node

i

to node

j

Input the coefficients, signs and RHS values in the answer boxes below:

Min Cost $=$

x

A

$1$

$+$

x

A

$2$

$+$

x

B

$1$

$+$

x

B

$2$

subject to:

x

A

$1$

$+$

x

A

$2$

$?$

x

B

$1$

$+$

x

B

$2$

$?$

x

A

$1$

$+$

x

B

$1$

$?$

x

A

$2$

$+$

x

B

$2$

$?$

x

A

$1$

$,$

x

A

$2$

$,$

x

B

$1$

$,$

x

B

$2$

$?$

$0$