King Henry V of England has decided to wage war on France and has engaged your services to assist him to assemble an appropriate army, which can consist of four types of troops: cavalry, men at arms, archers, 

and bombards (crude, and sometimes effective, artillery). Table 21.4 lists the weekly salary, offensive strength (OS), and defensive strength (DS) of each type of soldier
For example, if the army is composed of 50 cavalry, 100 men at arms, 100 archers, and one bombard, then we have:
\[\begin{aligned}& \text { Weekly cost }=50 \times 10+100 \times 5+100 \times 2+1 \times 20=1,220 \mathrm{GCs} \\& \mathrm{OS}=50 \times 30+100 \times 15+100 \times 20+1 \times 40=5,040 \\& \mathrm{DS}=50 \times 10+100 \times 20+100 \times 5+1 \times 0=3,000\end{aligned}\]
The King requests your advice on the composition of an army with the maximum possible OS but with DS of at least 7,000. The King is limiting his budget to 2,000 gold coins per week for this endeavor. Set up an LP and solve it.

Transcribed Image Text:

Table 21.4 Data for Each Type of Unit Unit Type Cavalry Men at arms Archers Bombards Cost/Week (gold coins) Offensive Strength (OS) 10 30 2528 15 20 20 40 Defensive Strength (DS) 10 2250