Optimizing a hypothetical factory system

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You have 1 factory that produces cars, and 1 "builder" factory that produces other factories (either car factories, or other builder factories; the latter take twice as long). You want to maximize the number of cars produced over 4 years. What is the optimal number of builder factories to produce before producing other car factories? “Builder” factories take a month to make, while car factories take half a month. Car factories produce a car a day.



I attempted to write a program that would try every number of “builder” factories up to 10000000, but I could not find a way to model the increase in production from previously constructed builders.




calculus optimization




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    You have 1 factory that produces cars, and 1 "builder" factory that produces other factories (either car factories, or other builder factories; the latter take twice as long). You want to maximize the number of cars produced over 4 years. What is the optimal number of builder factories to produce before producing other car factories? “Builder” factories take a month to make, while car factories take half a month. Car factories produce a car a day.



    I attempted to write a program that would try every number of “builder” factories up to 10000000, but I could not find a way to model the increase in production from previously constructed builders.




    calculus optimization




    share|cite|improve this question





















      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      You have 1 factory that produces cars, and 1 "builder" factory that produces other factories (either car factories, or other builder factories; the latter take twice as long). You want to maximize the number of cars produced over 4 years. What is the optimal number of builder factories to produce before producing other car factories? “Builder” factories take a month to make, while car factories take half a month. Car factories produce a car a day.



      I attempted to write a program that would try every number of “builder” factories up to 10000000, but I could not find a way to model the increase in production from previously constructed builders.




      calculus optimization




      share|cite|improve this question











      You have 1 factory that produces cars, and 1 "builder" factory that produces other factories (either car factories, or other builder factories; the latter take twice as long). You want to maximize the number of cars produced over 4 years. What is the optimal number of builder factories to produce before producing other car factories? “Builder” factories take a month to make, while car factories take half a month. Car factories produce a car a day.



      I attempted to write a program that would try every number of “builder” factories up to 10000000, but I could not find a way to model the increase in production from previously constructed builders.





      calculus optimization





      share|cite|improve this question










      share|cite|improve this question




      share|cite|improve this question









      asked Jul 21 at 14:44









      George Bidgood

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