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This question is based on the following table, which shows some parameters of various weapons used in role-playing gaming. Cost (gold pieces) Damage to Medium Targets Critical Weight (pounds) Weapon Damage Ахе 8 12 2 (Throwing) Javelin 1 6 12 2 Longsword 15 8 32 4 Mace (Light) 12 4 Spear 24 6 The Orc leader Achlúk has up to 100,000 gold pieces to spend on an arsenal of axes, maces, and spears for his army of orcs for a planned assault on Hobshire, in which he would like to inflict as much damage on medium targets (like humans and hobbits) as possible. To avoid excessive transportation costs, Achlúk needs to limit the total weight of the arsenal to 80,000 pounds or less, and, as his orcs are particularly fond of axes but not particularly skilled at spear-throwing, he would like to include at least as many axes as spears in the arsenal. What should his weapons arsenal look like?

This question is based on the following table, which shows some parameters of various weapons used in role-playing gaming. Cost (gold pieces) Damage to Medium Targets Critical Weight (pounds) Weapon Damage Ахе 8 12 2 (Throwing) Javelin 1 6 12 2 Longsword 15 8 32 4 Mace (Light) 12 4 Spear 24 6 The Orc leader Achlúk has up to 100,000 gold pieces to spend on an arsenal of axes, maces, and spears for his army of orcs for a planned assault on Hobshire, in which he would like to inflict as much damage on medium targets (like humans and hobbits) as possible. To avoid excessive transportation costs, Achlúk needs to limit the total weight of the arsenal to 80,000 pounds or less, and, as his orcs are particularly fond of axes but not particularly skilled at spear-throwing, he would like to include at least as many axes as spears in the arsenal. What should his weapons arsenal look like?

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter7: Systems Of Equations And Inequalities
Section7.2: Systems Of Linear Equations: Three Variables
Problem 58SE: At a carnival, $2,914.25 in receipts were taken at the end of the day. The cost of a child's ticket...
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This question is based on the following table, which shows some parameters of various weapons used in role-playing gaming. Cost (gold pieces) Damage to Medium Targets Critical Weight (pounds) Weapon Damage Ахе 12 (Throwing) Javelin 1 6. 12 2 Longsword 15 8 32 4 Mace (Light) 12 4 Spear 8 24 6. The Orc leader Achlúk has up to 100,000 gold pieces to spend on an arsenal of axes, maces, and spears for his army of orcs for a planned assault on Hobshire, in which he would like to inflict as much damage on medium targets (like humans and hobbits) as possible. To avoid excessive transportation costs, Achlúk needs to limit the total weight of the arsenal to 80,000 pounds or less, and, as his orcs are particularly fond of axes but not particularly skilled at spear-throwing, he would like to include at least as many axes as spears in the arsenal. What should his weapons arsenal look like? axes maces spears How much damage on medium targets can be inflicted? units of damage
Transcribed Image Text:This question is based on the following table, which shows some parameters of various weapons used in role-playing gaming. Cost (gold pieces) Damage to Medium Targets Critical Weight (pounds) Weapon Damage Ахе 12 (Throwing) Javelin 1 6. 12 2 Longsword 15 8 32 4 Mace (Light) 12 4 Spear 8 24 6. The Orc leader Achlúk has up to 100,000 gold pieces to spend on an arsenal of axes, maces, and spears for his army of orcs for a planned assault on Hobshire, in which he would like to inflict as much damage on medium targets (like humans and hobbits) as possible. To avoid excessive transportation costs, Achlúk needs to limit the total weight of the arsenal to 80,000 pounds or less, and, as his orcs are particularly fond of axes but not particularly skilled at spear-throwing, he would like to include at least as many axes as spears in the arsenal. What should his weapons arsenal look like? axes maces spears How much damage on medium targets can be inflicted? units of damage
Expert Solution
Step 1

Let x be the number of axes, y be the number of maces, and z be the number of spears. 

 

As the damage on the medium targets should be maximum, we have the objective function as

max 6x+6y+8z.

Gold Piece constraint: 8x+5y+2z≤100000

Weight constraint : 2x+4y+6z≤80000

Preferring ax over spear constraint: x≥z

and obviously, the number of weapons is positive, x,y,z's≥0.

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