Question Help

[lizzpalmer]

Here's my problem:

The average cost (in dollars) per item of manufacturing x thousand cans of spray paint is given by:

A(x) = -.000006x^4 + .0017x^3 + .03x^2 - 24x +1110

How many cans should be manufactured if the average cost is to be as low as possible? What is the average cost in that case?

I'm not sure how to get started on this one. Any help would be appreciated.

Lizz

 

[mmm4444bot]

Finding the exact value of x is a calculus exercise, unless you're supposed to use technology to estimate this value by zooming in on the local minimum point on the graph of function A.

Do you think that you're supposed to use a graphing calculator and zoom, to find the answer?

 

[lizzpalmer]

Yes it says to use my calculator.

 

[JeffM]

Yes it says to use my calculator.

Even calculus may require some approximation to find an exact NUMERIC answer. It depends on whether the real solutions of a cubic can be expressed in terms of radicals that are rational numbers.

 

[Deleted member 4993]

Here's my problem:

The average cost (in dollars) per item of manufacturing x thousand cans of spray paint is given by:

A(x) = -.000006x^4 + .0017x^3 + .03x^2 - 24x +1110

How many cans should be manufactured if the average cost is to be as low as possible? What is the average cost in that case?

I'm not sure how to get started on this one. Any help would be appreciated.

Lizz

I think you are supposed to use graphical method for this problem. Then investigate the graph to find minimum of A(x). Your answer should be an integer - somewhere between 70-80.

 

[mmm4444bot]

it says to use my calculator

Okay. I am assuming that you mean "graphing calculator" Did you use it?

I mean, you posted that you do not know how to get started on this exercise.

Plotting the graph and looking for the local minimum point is how to start. Use the features of the graphing calculator to then zoom in on the local minimum point, to see its coordinates.

 

[mmm4444bot]

Your answer should be an integer

The independent variable represents the number of thousands of cans.

If we talk about a value of x rounded to three decimal places, such as x = 4.123 (for example), would it be incorrect to say that this value of x represents 4,123 cans?

 

[Deleted member 4993]

Re:

Your answer should be an integer

The independent variable represents the number of thousands of cans.

If we talk about a value of x rounded to three decimal places, such as x = 4.123 (for example), would it be incorrect to say that this value of x represents 4,123 cans?

I missed the "thousand" cans part - thousands of apology - Denis I am on my way to the corner.....

 

[lizzpalmer]

Ok so, what do you mean by "zoom" on my calculator. I have a TI-83 Plus Texas calculator. There's a button that says zoom. Is that what we are talking about?

 

[lizzpalmer]

and if I'm supposed to enter this into my calculator I have no idea how. when I enter it and hit the zoom buttom it just comes up with an empty graph.

 

[mmm4444bot]

It seems like your on-line course might require basic graphing-calculator skills as a prerequisite.

"Zoom" means "enlarge", in graphing-calculator parlance. Your goal is to graph function A, and then enlarge the area of the graph at the minimum point. You can repeatedly zoom-in on any specific part of a graph, using the tools in that calculator, such that the coordinates of the traced points in that area are displayed with increasing precision (i.e., more and more decimal places displayed with each zoom-in).

You need to zoom-in far enough to get the x-value at the function's minimum point to display at least four decimal places so that you can round your answer to three decimal places.

If you have the User Manual for this calculator, the graphing instructions, features, and tools are described in Chapter 3.

:idea: The zoom-box feature is very helpful for enlarging a rectangular region that you draw on an already-displayed graph. You can read about this feature in Chapter 3, under the subheading "Exploring Graphs with the ZOOM Instructions".

If you do not have the manual, click here to download and save the manual in PDF format.

If you cannot access the PDF file, then let me know.

If you have any troubles understanding the manual, please post specific questions.

(Don't be afraid to experiment; you can't break the calculator by pressing "wrong" buttons. )