Doug C. answered • 07/11/22
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Doug C.
Hi Dwayn, As far as "always", it is pretty much the case to NEVER (hah, hah) use always. You just have to figure out what is being asked for and get that function defined. As I suggested, it is very rare in an optimization problem to not draw a diagram (at least for me). The video answer I provided did not use the 2nd derivative test, it simply used the 1st derivative test and identified x = 100 as creating a min value. The problem statement itself suggests that the critical number will generate a minimum, but it is a good idea to confirm that -- kind of serves as a double check that the "objective" function was defined correctly.
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07/11/22
Dwayn H.
Hello Doug, just to clarify, 3x +y is the perimeter correct.
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07/11/22
Doug C.
Perhaps best to think of that expression as the total length of fencing required, but I guess it does meet the definition of perimeter: the distance around the edge of a closed geometric shape.
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07/11/22
Dwayn H.
Hello Doug, I have a couple of questions. Is the perimeter the cost function in these type of problems? Do we always need to draw the picture to find the cost function? Also, do I need to do the first and second derivative test because I’ve seen a lot of different videos that have similar problems to this one, but they don’t do the first and second derivative test.07/11/22