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a. What is the optimal number of Orcs, Goblins and Uruks that Sauron can afford to employ and what is the greatest number of enemy troops that the assembled army can defeat? b. Can Sauron's army win the battle? Solve it using Simplex method, do not use any software.Show your work.

a. What is the optimal number of Orcs, Goblins and Uruks that Sauron can afford to employ and what is the greatest number of enemy troops that the assembled army can defeat? b. Can Sauron's army win the battle? Solve it using Simplex method, do not use any software.Show your work.

Practical Management Science
Practical Management Science
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ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
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Problem 4 Lord Sauron of Mordor is assembling an army of darkness against the human city of Gondor. He quickly finds out that this is not an easy task. It is a little known fact that Sauron is a civil rights leader to the Orc races, endeavoring to end a human imposed segregation once-and-for-all. As such, he is morally obligated to pay each member of his army a decent wage. There are three races of employable Orcs; the Orc, the goblin and the Uruk. Sauron has promised fair and non- discriminatory hiring practices and cannot exclude any race from his army. However there are population restrictions to consider. There are a total of 2200 employable Orcs, 3500 employable goblins and 2000 employable Uruk currently populating Mordor. Although Sauron will pay each troop equally, he realizes that it will cost more money to feed some of the Orc races than the others. A combined cost per Orcs, Goblin and Uruk is estimated to be $45, $30 and $105, respectively. Unfortunately Sauron has to consider the money available for war in the Morder treasurery, and cannot allow the cost to exceed $300,000. Sauron estimates that, on average, each Orc, Goblin and Uruk can defeat 1.65, 1.1, and 3.5 troops each, respectively. According to the Mordor armory, Sauron only has enough swords to arm 6,000 of his troops. Sauron estimates that there must be 12,000 enemy troops defeated in order to win the battle. a. What is the optimal number of Orcs, Goblins and Uruks that Sauron can afford to employ and what is the greatest number of enemy troops that the assembled army can defeat? b. Can Sauron's army win the battle? Solve it using Simplex method, do not use any software.Show your work.
Transcribed Image Text:Problem 4 Lord Sauron of Mordor is assembling an army of darkness against the human city of Gondor. He quickly finds out that this is not an easy task. It is a little known fact that Sauron is a civil rights leader to the Orc races, endeavoring to end a human imposed segregation once-and-for-all. As such, he is morally obligated to pay each member of his army a decent wage. There are three races of employable Orcs; the Orc, the goblin and the Uruk. Sauron has promised fair and non- discriminatory hiring practices and cannot exclude any race from his army. However there are population restrictions to consider. There are a total of 2200 employable Orcs, 3500 employable goblins and 2000 employable Uruk currently populating Mordor. Although Sauron will pay each troop equally, he realizes that it will cost more money to feed some of the Orc races than the others. A combined cost per Orcs, Goblin and Uruk is estimated to be $45, $30 and $105, respectively. Unfortunately Sauron has to consider the money available for war in the Morder treasurery, and cannot allow the cost to exceed $300,000. Sauron estimates that, on average, each Orc, Goblin and Uruk can defeat 1.65, 1.1, and 3.5 troops each, respectively. According to the Mordor armory, Sauron only has enough swords to arm 6,000 of his troops. Sauron estimates that there must be 12,000 enemy troops defeated in order to win the battle. a. What is the optimal number of Orcs, Goblins and Uruks that Sauron can afford to employ and what is the greatest number of enemy troops that the assembled army can defeat? b. Can Sauron's army win the battle? Solve it using Simplex method, do not use any software.Show your work.
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Step 1: Introduce the question:

For this question, First, I will formulate the Linear programming model, and then I will solve this LP using the simplex method, Initially, I will determine the optimal number of Orcs, Goblins, and Uruks and the greatest number of enemy troops that they can defeat. The rest of the answers are shown below, 


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