Quadractics

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tickalish_elmo

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Nov 16, 2007
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Here is the question:

The manager of a factory has found that the number of items produced per worker in the factory can be modeled by the following (use calculator)

T(x) = -.02x + 8x -24
where x is the number of workers at the factory on a given day, and T(x) is the
number of items produced per worker.

using the model find the following :

a) The number of workers needed to maximize the factory's output.
b) The maximum number of items the factory can produce in one day.

I don't know how to start the problem and how to plug in what is needed
to answer the questions, can you help me?
 
tickalish_elmo said:
Here is the question:

T(x) = -.02x + 8x -24
where x is the number of workers at the factory on a given day, and T(x) is the
number of items produced per worker.
Click to expand...

T(x) = -.02x + 8x -24 is not a quadratic function: please post the correct quadratic, as the tutor would only be guessing whether it is -0.2x^2 or 8x^2
 
The quadratic function's min or max will be at the vertex: x = -b/(2a) for a quadratic: ax^2 + bx + c

x = -b/(2a) is derived by completing the square, where (x + b/(2a))^2 can be expanded to a perfect square trinomial: We can find its x-coordinate from the fact that the square term above must be 0 at the vertex.

John
 
For the vertex I got v = (20, 120).
Does this tell me the max of the number of workers needed to maximize the output or the maximum number of items the factory can produce in one day?

Thank you so much for helping me .
 
tickalish_elmo said:
For the vertex I got v = (20, 120).
Does this tell me the max of the number of workers needed to maximize the output or the maximum number of items the factory can produce in one day?

Thank you so much for helping me .
Click to expand...

Double check that T(20) is what you say it is.

If x = # workers, than T(x) = ?
 
T(x) = The number of items produced per worker.

Im sorry I keep leaving info out.

would I plug 20 into the formula like this :
t(20)=-.2x^2 + 8x -24 ? and solve from there
to get the number of workers needed to maximize
the output?
 
tickalish_elmo said:
T(x) = The number of items produced per worker.

Im sorry I keep leaving info out.

would I plug 20 into the formula like this :
t(20)=-.2x^2 + 8x -24 ? and solve from there
to get the number of workers needed to maximize
the output?
Click to expand...

You already found the number of workers, remember? x = workers. You would plug in 20 into T(20) to get the products being produced. Think of it like solving x and y. You already solved for the coordinate for x, so plug x back in and get the coordinate for y... where y = T(x)
 
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