Optimisation Problem (maximizing production)

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f1player

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Feb 25, 2005
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A machine shop can produce 30 items a day on one machine. The shop can use more than one machine for the job, but if it does, for technical reasons each machine cannot then work to full capacity. In fact, production per machine is slowed by a factor equal to 1/10 of the square of the number of additional machines put on the job. That is, if x-additional machines are put on the job, the number of items produced by each machine is 30 - (x^2/10). How many machines should be used to achieve the maximum production?

I'm not even sure how to start this problem, any suggestions??
 
One thing good, they gave you the formula.

If x is the number of machines added and \(\displaystyle y=30-\frac{x^{2}}{10}\) is the number of items produced per machine, then the number of

items produced is xy.

Set up your function, differentiate, set to 0 and solve for x.
 
I managed to solve the problem myself. Thanks for the help anyway.
However, there is another question I have, similar to that one, that doesnt give you that equation.

Here it is:

A manufacturer knows that a production line with 24 workers can produce 100 units per worker per day. From experience, it is known that placing more people on the production line reduces the production of each worker by 2 units for every additional worker added to the line. How many workers should be placed on the line in order to maximise production?

I did this: Production = x(100-2x) , but didnt get the correct answer
 
f1player said:
However, there is another question I have....
Click to expand...
In future, please post new questions as new threads, not as replies to old threads, where they tend to be overlooked.

Thank you.

Eliz.
 
f1player said:
I managed to solve the problem myself. Thanks for the help anyway.
However, there is another question I have, similar to that one, that doesnt give you that equation.

Here it is:

A manufacturer knows that a production line with 24 workers can produce 100 units per worker per day. From experience, it is known that placing more people on the production line reduces the production of each worker by 2 units for every additional worker added to the line. How many workers should be placed on the line in order to maximise production?

I did this: Production = x(100-2x) , but didnt get the correct answer
Click to expand...

Stapel is correct. Please create your own thread from now on.

Anyway, try this instead:

\(\displaystyle (24+x)(100-2x)\)
 
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