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Bpp revision kit Q .89 MCQ
For this question the Answer says Option A”$1.50 per hour for the next 38,000 direct labour hours $1.50 per hour for the next 38,000 direct labour hours”. This is found by taking X as 10000units and find the new contribution of “95001.5”. So shadow price is 1.5$
However if we subsititte Y as 12,000 in the equation “5x+4y=60000 the optimal production plan is Y=12,000 and X=2400.2 units which gives a total contribution of “91201.6”. Here the shadow price is “$1.6”.
Ideally whichever way we substitute i.e X in equation or Y in the quation, we should get same shadow price right?.Moreover the above units are withing the given constraints.
Can you please explain why there is a difference in the answer or is my understanding incorrect?
Ok no need sir, i got it. You wont get the same answer.
But for exam can we assume that labour hours for Y is increasing and find the shadow price?
And since the above is an MCQ question how do we understand that X needs to be substituted instead of Y? Will we get the marks if we give shadow price as”$1.60 per hour for the next 38,000 direct labour hours”
Thanks in advance
The limiting constraints at the optimal solution are x < 10,000 and 5x + 4y < 60,000, so to calculate the show price you have to use these constraints. (y < 12,000 is not a limiting constraint at the optimal solution).
Have you watched my free lectures on linear programming? The lectures are a complete free course for Paper PM and cover everything needed to be able to pass the exam well.
Thank you sir , but i dnt understand how Y is not a limiting constraint here? becuase the question says Y<12,000.
I did watch the lectures but im still not able to grab why Y is not a onstraint?The question says that the optimal solution is 10000 of X and 2500 of Y.
Given the the Y constraint is that Y must be less than 12,000, and given that the optimal solution is only producing 2,500 of Y, then the Y constraint is not a limiting constraint.
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