You have provided no new information. All of this was understood by the OP before he even posted his question. The posted replies also addressed all of this again since we didn't realize he had correctly solved the problem that he posted according to his interpretation. Now you have just reiterated it all again in greater detail, since you clearly did not read the responses, or scanned them too quickly. (which is fine, as you may be busy)If you look at the spreadsheet you can see clearly that for a, b =18, 24 the minimum does not occur at r=0
In fact since only the walkway contributes to the variation in area for values of r less than 3 we want to maximise the side with the area b*r and miniimise the side with the area 3*a
Similarly for r>3 we want to minimise rb and maximise 3a.
This also shows up clearly in the spreadsheet. I can't draw a graph as it is a 4 dimensional figure.
However the minimum value of area occurs at a different pair of values for a,b for every value of
Notice r cannot be zero or infinity as that would require b or a to be infinity and the other to be zero at the minimum 'area'
This question contains more than meets the eye.
The mystery is whether the drawing the OP provided represents a correct interpretation of the problem as quoted from the book. If so, the book answer is wrong. If not, what is the correct interpretation?
I'm not sure if the OP cares anymore as he should realize that he has a good understanding of the material he is studying. Personally, I could just dismiss the problem as a poorly worded question, but also I'm curious if there is another interpretation of the words that leads to the book's numerical answer. Perhaps you can focus your considerable intellect on this latter issue? I ask respectfully. I tried and failed, and if no one else cares to pursue it, then there is not much more to address in this thread.