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Optimizing production for hypothetical factories [closed]
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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?
Edit: “Builder†factories take a month to make, while car factories take half a month. Car factories produce a car a day.
calculus optimization
asked Jul 19 at 22:17
George Bidgood
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closed as off-topic by Somos, Xander Henderson, Adrian Keister, Isaac Browne, Parcly Taxel Jul 20 at 2:58
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Xander Henderson, Adrian Keister, Isaac Browne, Parcly Taxel
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up vote
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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?
Edit: “Builder†factories take a month to make, while car factories take half a month. Car factories produce a car a day.
calculus optimization
asked Jul 19 at 22:17
George Bidgood
264
closed as off-topic by Somos, Xander Henderson, Adrian Keister, Isaac Browne, Parcly Taxel Jul 20 at 2:58
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Xander Henderson, Adrian Keister, Isaac Browne, Parcly Taxel
add a comment |Â
up vote
5
down vote
favorite
up vote
5
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?
Edit: “Builder†factories take a month to make, while car factories take half a month. Car factories produce a car a day.
calculus optimization
asked Jul 19 at 22:17
George Bidgood
264
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?
Edit: “Builder†factories take a month to make, while car factories take half a month. Car factories produce a car a day.
calculus optimization
asked Jul 19 at 22:17
George Bidgood
264
edited Jul 20 at 1:45
asked Jul 19 at 22:17
George Bidgood
264
asked Jul 19 at 22:17
George Bidgood
264
asked Jul 19 at 22:17
George Bidgood
264
264
closed as off-topic by Somos, Xander Henderson, Adrian Keister, Isaac Browne, Parcly Taxel Jul 20 at 2:58
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Xander Henderson, Adrian Keister, Isaac Browne, Parcly Taxel
closed as off-topic by Somos, Xander Henderson, Adrian Keister, Isaac Browne, Parcly Taxel Jul 20 at 2:58
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Xander Henderson, Adrian Keister, Isaac Browne, Parcly Taxel
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1 Answer
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There is not enough data for a meaningful answer; in particular, missing data include how long it takes to produce a factory, and how long it takes to produce a car.
For example, suppose producing a car factory takes 1 year, and a car also 1 year. Then, clearly, you should stop producing builder factories no later than 2 years down the road, as all builder factories finished after this time will not yield a single car. This means that you should not have more than 2 builder factories before switching to producing car factories.
Suppose instead that building a car factory takes 1 day, and a car 1 hour.
It is not difficult to see that switching to car factories at any time during the first $3$ years is going to slow reduce car production: spendng 1 more month producing builder factories will yield more than 1000 times as many cars. Then, you are going to have far, far, far more than 2 builder factories by the time you hit the 3-year mark.
answered Jul 19 at 22:37
Anonymous
4,8033940
I think the OP says that producing a car factory take twice as long as producing a car, so your examples might be a bit off. However, I agree with your initial point.
– Theoretical Economist
Jul 19 at 23:01
Isn't there a generalization here? That is, doesn't your objection apply to all rates of car and factory production? If we assume a car production rate r, then optimize the point within 48 months of switching from producing factories for making car factories to car factories (at double the rate) to maximize a multiple of r.
– Phil H
Jul 19 at 23:09
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
There is not enough data for a meaningful answer; in particular, missing data include how long it takes to produce a factory, and how long it takes to produce a car.
For example, suppose producing a car factory takes 1 year, and a car also 1 year. Then, clearly, you should stop producing builder factories no later than 2 years down the road, as all builder factories finished after this time will not yield a single car. This means that you should not have more than 2 builder factories before switching to producing car factories.
Suppose instead that building a car factory takes 1 day, and a car 1 hour.
It is not difficult to see that switching to car factories at any time during the first $3$ years is going to slow reduce car production: spendng 1 more month producing builder factories will yield more than 1000 times as many cars. Then, you are going to have far, far, far more than 2 builder factories by the time you hit the 3-year mark.
answered Jul 19 at 22:37
Anonymous
4,8033940
I think the OP says that producing a car factory take twice as long as producing a car, so your examples might be a bit off. However, I agree with your initial point.
– Theoretical Economist
Jul 19 at 23:01
Isn't there a generalization here? That is, doesn't your objection apply to all rates of car and factory production? If we assume a car production rate r, then optimize the point within 48 months of switching from producing factories for making car factories to car factories (at double the rate) to maximize a multiple of r.
– Phil H
Jul 19 at 23:09
add a comment |Â
up vote
0
down vote
There is not enough data for a meaningful answer; in particular, missing data include how long it takes to produce a factory, and how long it takes to produce a car.
For example, suppose producing a car factory takes 1 year, and a car also 1 year. Then, clearly, you should stop producing builder factories no later than 2 years down the road, as all builder factories finished after this time will not yield a single car. This means that you should not have more than 2 builder factories before switching to producing car factories.
Suppose instead that building a car factory takes 1 day, and a car 1 hour.
It is not difficult to see that switching to car factories at any time during the first $3$ years is going to slow reduce car production: spendng 1 more month producing builder factories will yield more than 1000 times as many cars. Then, you are going to have far, far, far more than 2 builder factories by the time you hit the 3-year mark.
answered Jul 19 at 22:37
Anonymous
4,8033940
I think the OP says that producing a car factory take twice as long as producing a car, so your examples might be a bit off. However, I agree with your initial point.
– Theoretical Economist
Jul 19 at 23:01
Isn't there a generalization here? That is, doesn't your objection apply to all rates of car and factory production? If we assume a car production rate r, then optimize the point within 48 months of switching from producing factories for making car factories to car factories (at double the rate) to maximize a multiple of r.
– Phil H
Jul 19 at 23:09
add a comment |Â
up vote
0
down vote
up vote
0
down vote
There is not enough data for a meaningful answer; in particular, missing data include how long it takes to produce a factory, and how long it takes to produce a car.
For example, suppose producing a car factory takes 1 year, and a car also 1 year. Then, clearly, you should stop producing builder factories no later than 2 years down the road, as all builder factories finished after this time will not yield a single car. This means that you should not have more than 2 builder factories before switching to producing car factories.
Suppose instead that building a car factory takes 1 day, and a car 1 hour.
It is not difficult to see that switching to car factories at any time during the first $3$ years is going to slow reduce car production: spendng 1 more month producing builder factories will yield more than 1000 times as many cars. Then, you are going to have far, far, far more than 2 builder factories by the time you hit the 3-year mark.
answered Jul 19 at 22:37
Anonymous
4,8033940
There is not enough data for a meaningful answer; in particular, missing data include how long it takes to produce a factory, and how long it takes to produce a car.
For example, suppose producing a car factory takes 1 year, and a car also 1 year. Then, clearly, you should stop producing builder factories no later than 2 years down the road, as all builder factories finished after this time will not yield a single car. This means that you should not have more than 2 builder factories before switching to producing car factories.
Suppose instead that building a car factory takes 1 day, and a car 1 hour.
It is not difficult to see that switching to car factories at any time during the first $3$ years is going to slow reduce car production: spendng 1 more month producing builder factories will yield more than 1000 times as many cars. Then, you are going to have far, far, far more than 2 builder factories by the time you hit the 3-year mark.
answered Jul 19 at 22:37
Anonymous
4,8033940
edited Jul 19 at 22:43
answered Jul 19 at 22:37
Anonymous
4,8033940
answered Jul 19 at 22:37
Anonymous
4,8033940
answered Jul 19 at 22:37
Anonymous
4,8033940
4,8033940
I think the OP says that producing a car factory take twice as long as producing a car, so your examples might be a bit off. However, I agree with your initial point.
– Theoretical Economist
Jul 19 at 23:01
Isn't there a generalization here? That is, doesn't your objection apply to all rates of car and factory production? If we assume a car production rate r, then optimize the point within 48 months of switching from producing factories for making car factories to car factories (at double the rate) to maximize a multiple of r.
– Phil H
Jul 19 at 23:09
add a comment |Â
I think the OP says that producing a car factory take twice as long as producing a car, so your examples might be a bit off. However, I agree with your initial point.
– Theoretical Economist
Jul 19 at 23:01
Isn't there a generalization here? That is, doesn't your objection apply to all rates of car and factory production? If we assume a car production rate r, then optimize the point within 48 months of switching from producing factories for making car factories to car factories (at double the rate) to maximize a multiple of r.
– Phil H
Jul 19 at 23:09
I think the OP says that producing a car factory take twice as long as producing a car, so your examples might be a bit off. However, I agree with your initial point.
– Theoretical Economist
Jul 19 at 23:01
I think the OP says that producing a car factory take twice as long as producing a car, so your examples might be a bit off. However, I agree with your initial point.
– Theoretical Economist
Jul 19 at 23:01
Isn't there a generalization here? That is, doesn't your objection apply to all rates of car and factory production? If we assume a car production rate r, then optimize the point within 48 months of switching from producing factories for making car factories to car factories (at double the rate) to maximize a multiple of r.
– Phil H
Jul 19 at 23:09
Isn't there a generalization here? That is, doesn't your objection apply to all rates of car and factory production? If we assume a car production rate r, then optimize the point within 48 months of switching from producing factories for making car factories to car factories (at double the rate) to maximize a multiple of r.
– Phil H
Jul 19 at 23:09
add a comment |Â