Use R studio to solve the following problem

You plan to play a game using Neil Thomas' Ancient and Medieval Warfare rules. You decide to take the Parthian army. The Parthian army has the following minimums and maximums.

2 to 4 units of Nobles - Heavy Cavalry, Extra Heavy Armor, Elite

4 to 6 units of Horse Archers - Light Cavalry (bow), Light Armor, Average

0 to 2 units of Milita - Light Infantry (javelin), Light Armor, Levy

Your opponent decides to take the following army

Alexandrian Macedonian

5 units of Phalangites - Heavy Infantry, Medium Armor, Average

2 units of Companions - Heavy Cavalry, Light Armor, Elite

1 unit of Thessalians - Light Cavalry (javelin), Light Armor, Elite

You believe the best way to defeat this army is with highly mobile units that have archery (bows). Therefore, you give 1 point for every inch in movement, 1 point for every unit that has bows, and a half (.5) points for every attack die.

Parthian Nobles move at a rate of 6. Light Horse move at a rate of 12. Militia move at a rate of 4.

You must calculate total Attack Dice. This means you will take the number of attack dice for the three unit types in the Parthian army against the three unit types in your opponent's army, the Alexandrian Macedonian army. Much like I did for in the MS Excel example. Attack Dice can be determined using slide #8 of the lecture for any given match-up between two units.

Using the constrOptim function in R, calculate the configuration of Parthian army units that maximizes total points: 1 point for every inch in movement, 1 point for every unit that has bows, and a half (.5) points for every attack die.

Hint -- work through using the following steps

Step 1 - Develop a 3 by 3 matrix for number of attack dice on paper for easy reference

Step 2 Write out the objective function

Step 3 Write out the constraints in terms of the max and min values and decision variables

Step 4 Write out the ui and ci matrices

Step 5 Enter it all into R and solve the problem

PARTHIAN ARMY (250 BC-AD 225) Unit type Number per army 2-4 4-6 0-2 Nobles (Heavy Cavalry, extra-heavy armour, Elite) Horse Archers (Light Cavalry (bow), light armour, Average) Militia (Light Infantry (javelin), light armour, Levy) For cavalry lovers, the Parthians have to be the army of choice. These heirs to Achaemenid territory (and monarchical style of government) shared the Persian predilection for mounted warfare to a truly spectacular degree. The wargames general should be aware that getting the balance right between the fire and shock combat is essential, if success is to ensue. SPECIAL RULES Parthian nobles. With both man and horse enjoying the benefits of heavy armour, the nobles' movement was inevitably compromised. Accordingly their movement rate is reduced to 12cm per turn 1) 2) Foot archers. The Parthians seem to have made some use of archery in their militia. If two units are fielded, one of them may be equipped with bows instead of javelins. PARTHIAN ARMY (250 BC-AD 225) Unit type Number per army 2-4 4-6 0-2 Nobles (Heavy Cavalry, extra-heavy armour, Elite) Horse Archers (Light Cavalry (bow), light armour, Average) Militia (Light Infantry (javelin), light armour, Levy) For cavalry lovers, the Parthians have to be the army of choice. These heirs to Achaemenid territory (and monarchical style of government) shared the Persian predilection for mounted warfare to a truly spectacular degree. The wargames general should be aware that getting the balance right between the fire and shock combat is essential, if success is to ensue. SPECIAL RULES Parthian nobles. With both man and horse enjoying the benefits of heavy armour, the nobles' movement was inevitably compromised. Accordingly their movement rate is reduced to 12cm per turn 1) 2) Foot archers. The Parthians seem to have made some use of archery in their militia. If two units are fielded, one of them may be equipped with bows instead of javelins