# Number of Troops Assignment | Assignment Help Services

One of the factors that contribute to the success or failure of a particular army during war is its ability to get new troops ready for service. It is possible to analyze the rate of change in the number of troops of two hypothetical armies with the simplified model

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Rate of increase (Red Army)=200,000 – .5r – .3b

Rate of increase (Blue Army)=350,000 – .5r – .7b

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where r is the number of soldiers in the Red Army at any given time and b is the number of soldiers in the Blue Army at the same time. The factors .5 and .7 represent each army’s efficiency at bringing new soldiers into the fight.

a) Solve this system of equations the determine the number of soldiers in each army when the rate of increase for each is zero.

b) Describe what might be going on in a war when the rate of increase is zero.

Answer a)Since rate of increase for each army (RED and BLUE) is zero, the system of equationbecomes￬ 0 =200000 – 0.5r – 0.3b￬￬ 0 =350000 – 0.5r – 0.7bOr￬ 0.5r +0.3b =200000￬￬..

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