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Untimely Explosions (Second Problem)
An Ordnance Decision Game
If you have not done so already, please read the first two posts in this series.
Solution to the First Problem
You decide that you are far too busy with the task of acquiring ordnance to focus on the problem of premature explosions. You therefore ask a senior subordinate, Fernand-François Gossot, to conduct a detailed inquiry into the problem.
Brigadier General Gossot, who holds a masters degree in mathematics, has made a number of important discoveries related to interior ballistics. When not teaching mathematics at the École Polytechnique or conducting experiments in ballistics, he has commanded artillery units of the Troupes de la Marine and supervised the manufacture of naval ordnance.
The Second Problem
It is now 20 January 1915.
At present, French factories are producing, each day, 63,000 explosive shells for 75mm field guns. Of these, 22,500 shells are made by experienced factories, 40,500 by new factories.
Earlier today, General Gossot provided you an interim report of his findings. These are:
Between 2 August 1914 and 20 December 1914, 75mm field guns of the French Army fired 3,000,000 explosive shells. Of these projectiles, six exploded before leaving the barrel of the gun that fired them. Thus, for every 500,000 explosive shells fired, one exploded prematurely.
On 20 December 1914, batteries at the front began to take delivery of explosive shells made by new factories.
Since 20 December 1914, the rate of premature explosions has increased from one in 500,000 to one in 5,000.
General Baquet, what is going on here? What is your plan?
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