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# Our Cause

We develop advanced weapons and grenades to secure victory in any war no matter what. Our professionally trained fighters are given a wide variety of tactics and skills to properly use our technology. Once squad leaders and their patrol graduate the training program, they must find sponsors to raise 10,000 dollars so they can purchase their select arsenal of weaponry.

# The Options

The squad leaders are only in charge of their men and themselves. All submachine guns sell for \$800 and all assault rifles are \$600. The squad leaders are trained to always have at least 2 more assault rifle marksmen than submachine gun soldiers. Our scientists are only able to make a maximum of 9 of each weapon. It is expected that the squads use their money to get the most amount of weapons possible.

Assault Rifle Courtesy of Advanced Warfare
Submachine Gun Courtesy of Nexonuen

# The Restrictions

X= # of Submachine Guns

Y= # of Assault Rifles

X≥0

Y≥0

X≤9

Y≤9

800x+600y≤10,000

x≥y+2

Things to Know

Profit=300x+200y

Max. Weapon Amount=x+y

Cost=500x+400y

# Analyzing the Equation

Maximum Weapons

(2)+(0)=2

(9)+(0)=9

(9)+(4.67)=13.67

(8)+(6)=14

Profit

300(2)+200(0)=\$600

300(9)+200(0)=\$2,700

300(9)+200(4.67)=\$3,634

Rounding 4.67 to 4=\$3,500

300(8)+200(6)=\$3,600

# The Best Option

For both getting the most profit and the most weapons best works with buying 8 assault rifles and 6 submachine guns. The squads would get a total of 14 weapons, and  the company would make \$3,600. Though \$3,600 does not supply enough money to cover the costs F.O.A.F. is able to makes most of its money from winning wars, and dealing with terrorists, but the extra money from the sponsors does help.