please answer this in excel or with QM: The Battle of the Bulge

On December 16, 1944, in the last year of World War II,

two German panzer armies, supported by a third army of

infantry, together totaling more than 250,000 men, staged

a massive counteroffensive in northern France, overwhelming

the American First Army in the Ardennes. The

offensive emanated from the German defensive line along

the Our River, north of the city of Luxembourg, and was

directed almost due west toward Namur and Lige in Belgium.

The result, after several days of fighting, was a huge

bulge in the Allied line and, therefore, this last major

ground battle of World War II became known as the Battle

of the Bulge.

On December 20, General Dwight D. Eisenhower,

Supreme Allied Commander, called on General George Patton

to attack the German offensive with his Third Army,

which was then situated near Verdun, approximately 100

miles due south of the German left flank. Pattons immediate

objective was to relieve the 101st Airborne and elements

of Pattons own 9th and 10th Armored Divisions surrounded

at Bastogne. Within 48 hours, on December 22, Patton was

able to begin his counteroffensive, with three divisions totaling

approximately 62,000 men.

The winter weather was cold with snow and fog, and the

roads were icy, making the movement of troops, tanks, supplies,

and equipment a logistical nightmare. Nevertheless, on

December 26 Bastogne was relieved, and on January 12,

1945, the Battle of the Bulge effectively ended in one of the

great Allied victories of the war.

General Pattons staff did not have knowledge of the

maximal flow technique nor access to computers to help

plan the Third Armys troop movements during the Battle of

the Bulge. However, the figure on the following page shows

the road network between Verdun and Bastogne, with

(imagined) troop capacities (in thousands) along each road

branch between towns. Using the maximal flow technique

(and your imagination), determine the number of troops that

should be sent along each road in order to get the maximum

number of troops to Bastogne. Also indicate the total number

of troops that would be able to get to Bastogne