Good day everyone, I am not a mathematics major or student and I thus apologise for my mathematical ineptitude. I am a business student researching optimal economic replacement problem of capital equipment in the mining industry in South Africa. Please bear with me and I will really appreciate any assistance from the maths community. One aspect of my research yielded an equipment maintenance cost function overtime as being:
y=2.71x10^-7.x^3-3.629x10^-3.x^2+119.802.x-62.484x10^3 for my model, X reflects the equipments cumulative age in hours and y being the cumulative repair & maintenace cost of the aforementioned. I have obtained this model by carrying out non linear regression analysis of the data on hand.
I am trying to do the following: If I increase the y2 value (increase cost) at x2 and I keep the x1 & y1 values as they are, how would I go about determining what the coeffficents are, i.e. a0,a1,a2,a3 etc. In essence, I would like to plot another polynomial function that would fit the same initial points as what the initial polynomial equation reflected, x1 and y1 will be the same for the new equation. X2 would also be the same, but Y2 would have a different value. In summary to make sure that I am expressing myself clearly. I will have two polynomial graphs, i.e. one being the one indicated above and the second will have a different y2 value. This function also needs to be a polynomial function. Please if anyone out there can help me, I will really appreciate the assistance.
I will ad more context to the question and explain more clearly what I am trying to achieve. Having obtained the non linear regression model as indicated earlier, I can now calculate the anticipated value of y (i.e. repair & maintenance expense of the asset) at a specific time , i.e. X. This function is thus a polynomial function. I can then include these expenses into my NPV model and thus observe how these values effect the overall NPV of the model.
Referring to the initial model reflected, I have included the estimated coefficients, viz.: a0,a1,a2,a3 etc. From this model, I can obtain the slope (k1) at x1 the slope (k2) at x2
I am trying to do the following.
I would like to plot another polynomial function that originates from the same coordinates at the first function referred to earlier, i.e. coordinates (x1 &y1) will be the same as the new curve I would like to plot. The end point of the curve however will only have the same x2 coordiante, but a different Y2 coordinate.i.e. an increased Y2 value.
So essentially I will know what the (x1;Y1) coordinate of teh first point on teh curve is. I will also know what the second coordinates are of the end point of the new curve.
I am thus trying to identify what the new coefficients would be of the new polynomial equation would be, i.e. what the equation would be.
Once I know what the second polynomial curve equation is, I can then plot the aforementioned.
So if I had to superimpose the two polynomial curves, i.e. regression function indicated, From the second curve, I will now be able to identify what the predicted repair and maintenance expenses would be given the new scenario, i.e. steeper slope and hence different coefficients.
Hope this clarifies the question a little more.
