math solution needed

I hope there's someone here good at math. I generally am but this problem stumps me.
The blue graph is the result of mutiplying the green and red graphs together. That gives me the correct beginning and end but I want the middle to dip down to correspond with where the green and red graphs cross. Any suggestions?
BlairHP2.gif

First, I believe your assumption is incorrect that the blue line has a dip in it. Why do you think that should be? When I construct two straight lines that look kind of like yours, the product is parabolic, with the max value right where the lines cross.

Please attach your file so we can see the data.

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If the blue graph must be the product (or a function of the product) of the red and green curves, then the only way to get the "double hump" is for the values of the red and green curves to give that shape. What are the values for the red and green curves? What is the relationship between the blue curve and the red and green curves? Can you change or edit the values of the red and green curves to give the desired shape?

So, the blue curve is not strictly limited to red*green*1.5 -- you can use any combination of red and green to get blue that gives the right shape. Is that right?

For a purely empirical approach, we can use our favorite tool -- polynomials. The desired shape of the purple curve will require at least a 4th order polynomial. I might start by fixing the location of the minima and maxima (the zeroes of the first derivative) and find a cubic expression for the first derivative (http://www.purplemath.com/modules/fromzero2.htm ). From the cubic first derivative, take an antiderivative to get the resulting quartic equation that should have the correct shape. Then work on what the red and green curves should look like to give the desired blue curve.

How can anyone help when you haven't told us the calculations that you are making that you now say might be wrong?

Please mind your tone. We are here to help and do so voluntarily. You will alienate helpers with your attitude if you are not careful.

I was referring to this statement, which requires some extra explanation from you:

Keep in mind that the solution to my problem may be in how I am calculating for the green and red graphs.

We do not know how you are calculating these - you have not told us.

Nobody is trying to divert. We are asking for clarification from you so that we can help. There has been no silence - you have (had) two members engaging with your problem, but have failed to provide either the worksheet or the other information requested (posts #2 and #12). Yes, of course it is impossible for us to help without all the necessary data. This does not mean that members here are incapable of solving your problem, but you do need to do what they ask of you if you want their help. It's up to you, really.

I did not carry through to a final solution, so I cannot show you my final equation. I started with (as illustrated in the algebra tutorial I linked to):

1) dy/dx=-1*(x-10500)*(x-11250)*(x-12000) I picked these "roots" from the purple curve you drew on the chart. It should be easy to see that dy/dx=0 whenever x=10500 or x=11250 or x=12000. The -1 multiplier I think is necessary so that the final quartic will be concave down rather than concave up. Recall from your calculus classes that the points where dy/dx=0 are the maxima/minima of y=f(x)
2) Multiply that out to get dy/dx=ax^3+bx^2+cx+d
3) "Solve" the differential equation by getting an antiderivative for dy/dx. If you have forgotten how to take antiderivatives of polynomials: http://www-math.mit.edu/~djk/calculu...section01.html you should end up with something of the form y=Ax^4+Bx^3+Cx^2+Dx+E. You will probably need to arbitrarily choose a value for E.
4) Try to figure out what kind of equations for the red and green curves can be combined to give the quartic obtained in (3).

All of that assumes that polynomials are the best model -- which may or may not be true. We often use polynomials when we don't know any better just because they are flexible and easy to work with. I could also see trying trig functions (perhaps a Fourier regression) or who knows what else. Ultimately, this comes back to what 6stringjazzer is saying -- sometimes one needs to get at the engineering side of this and really understand the functions that should be used and how they should be combined.