You're welcome, Vivid.

Good point. Thanks.

+itsdannyftw You are right. I should have shown how. I was trying to cut down the video length as much as possible. It is always better to test. But I guessed I simply applied one of the rules I suggested against; "if the negative sign is only on the x coefficient, then treat the situation as normal. If it is only on the y coefficient, go the other direction." The example you gave "-3x + 2y ≤ -4" is the same as "3x - 2y ≥ 4". I guess I shouldn't be saying "toward the origin". I actually didn't mean it as a rule; I was only trying to describe the direction. Thanks for bringing this up. It'll help clean up my act a little bit.

+Joshua Emmanuel Thanks for clarifying. Also, could you refer me to the video where you stated those rules? I don't recall you mentioning them in any of the LP series videos. In addition, I suppose those rules can get a little messy, i.e. do they only apply when the equations are in standard form, and not when in slope-intercept form? And like in the example I gave, when or how would we know which is the appropriate equation we should be using? i.e. even though "-3x + 2y ≤ -4" is the same as "3x - 2y ≥ 4", why is it that we need to make this distinction (or put another way, 'convert' it to another equivalent equation/form)? I don't understand; is it simply to be able to apply the "rules" and thus to determine which direction to shade? Actually I think I misunderstood the rule, I thought we were looking at the negative signs on only either of the two coefficients, but rather I think the rule suggests to have only one negative sign on the entire equation? i.e. in this case, although there is only one negative sign on the x coefficient, thus, we should 'treat the situation as normal', we need to notice that there is also a negative sign on the '4', hence why you multiplied the equation by -1, in order to be able to 'conform' to the rule requirements which enables you to apply the rule? Evidently, if so, having these 'rules' does make the process more complicated than it actually is. And rather, it seems to be always best to test points, like you have mentioned previously. Or have I misunderstood and to be efficient at solving these problems, you really ought to just persevere in applying those rules? Thanks again.

I actually never mentioned those rules in any of my videos. And yes, rewriting the the constraint is simply an attempt to fit it to one of the modes the rules apply to. My Verdict: Testing points is the best way to go.

+Joshua Emmanuel Excellent, thank you. May I ask how did you arrive at that rule you quoted then? Is it just from experience? Out of experimentation, I attempted to try it out on this constraint equation: 3x - 2y ≤ 4 which ultimately gets shaded to the left (or 'above') the line. However applying what you stated earlier that, "if [the negative sign] is only on the y coefficient, go the other direction." If that rule were to be applied here, wouldn't we be shading to the right or 'below' the line (since that is the 'other direction' for a less than or equal to constraint)? Is this a scenario where I have incorrectly applied the rule or it's a scenario where I have encountered an exception to the rule (and thus again, clearly elucidates why you don't advocate the use of these 'rules')? I assume the former, and hope you could clarify.

Yeah, the rules come by observation. "Above the line" is the "other direction" for a ≤ constraint by the way. And, did I say forget the rules? What you call "above" sometimes may actually be "below", depending on the objective. Test the points, and you can never go wrong.

You're welcome Khaled

Joshua Emmanuel nice

You forget to add "King"...haha.

Joshua Emmanuel haha I just watched this before writing the exam and I forgot that King part I might have typed it in a rush so yah ... Hail King Joshua !!!

Lovely! You're amazing. Thanks for the comments.

Can you include the time stamp

Go to the link below. Click Solve Model at the bottom left corner. Click Model Overview to see the graph and objective function value. online-optimizer.appspot.com/?model=ms:jg10guIKiyf2t2YJEgJawGH3RBanu8s1

@@joshemman thank you so much (from Morocco 🇲🇦)

@@cherdoudayoub5755 My pleasure