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Limiting factors – Linear Programming

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  1. Hi, I have a question. I never really concentrated on this, until I met the way you did the programming. I usually put x and y as variables and graph them correspondingly (x axis and y axis). This time I put S and E as you have done and put S on x axis and E on Y axis and got totally different graph from the one you got. What is the right way to go.? I know this question may seem primitive, but I decided to ask. Thanks in advance.

  4. Sir, in the lectures, you said that maximum contribution is at point B which is correct and same was also proven when you have calculated the max cont at point A. But Sir my question is, “in the graph, on what basis you have said that B is the best point”. Because if i am not mistaken, in the lecture, you firstly said that B is the best point and then you have calculated the max cont and then you have shown the difference in contribution between point A and B.

    Thank you for your help Sir.

  5. Sir, thank you for the fabulous lectures, it really helps.
    However i am confuse about one thing. In the Question 1, the requirement is firstly ‘Find the optimal production plan’ does the answer is the feasible region drawn in the graph.

    In addition, kindly advise why do we calculate ISO contribution? Why must we draw the ISO contribution line in the graph.

    Thanks to help Sir.

    • The feasible region identifies which combinations of the two products satisfy the constraints.

      We need the contribution line to find out which of these combinations is the optimal (i.e. gives greatest contribution). We move the line as far away from the original as possible and the optimum is the corner of the feasible region furthest away.

  8. 6s+9E= $ 225 (S=0 ; E= 25) ( E=0 ; S= 37.5)
    since Contribution comes out of to be $225, if we check the the contribution if it is out of the red shaded bodx or not it is actually is, i did not get it is..

      • It is not a question of whether or not the contribution is inside or outside the box!! That does not make sense.

        The optimum mix is at point b – the point furthest away from the origin. This point is on the edge of the feasible region.

        When we know what the values are at that point then we can calculate the contribution.

        The values stated by Imran for S and E were purely for being able to draw the contribution line – there is no other relevance of them.

  10. Dear John,
    The example you’ve shown here is a 3rd example, which I encounter since I study F5, where the highest profit is earned at the intersection of labour hours and machine hours lines. Is this a rule? If yes, why don’t we go straight to that intersection?
    Why did you say that that the any of the corners could be most profitable?

    • No it isn’t a rule. The highest contribution will be earned at whichever of the corners is the furthest away from the origin when moving out the iso-contribution line.

      If you watch the video again you will see that if the line were a different angle, then when it is moved out then a different corner could be the furthest away.

      If you are not sure what I mean, just suppose the question was exactly the same except that the contribution per unit for S was $10, and for E was $1. The constraints are all the same and so the graph is the same.
      However, point A would then give the highest contribution ($360). Point B would only give a contribution of $305.

  17. Hiii sir, your lectures juz awesome 馃榾

    I have a question… Will be my answer considered wrong if thers a diffrnce in my optimal solution,whethr if i use “inspection” or “drawing ISO contribution line”?

    • It depends what you mean by ‘inspection’.
      The only alternative to drawing the iso-contribution line is to calculate the total contribution at ever corner of the feasible area.
      (But still read the question carefully – obviously if it specifically asks for you to draw the iso-contribution line, then there is no choice 馃檪 )

  18. Hello sir . Very nice lecture 馃檪 .. Sir i have a question .. That why we made third equation ? And what is its link with point B ? And sir if its all about calculating equations then why we plot graph .. Why we dont do all this in the begining ? Thankyou sir 馃檪

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