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In a linear programming problem to determine the production and sales volumes to maximize contribution of the two products, H and L, the following information is available.
Product H. 4 HRS. 2KG Contribution per unit. 14$
Product L. 2HRS. 4KG Contribution per unit. 20$
12.000 hrs 16.000 kg. available.The profit-maximizing level of output and sales is 7,333 units of Product H and 3,334 units of Product L.
What is the shadow price of a direct labour hour? (Correct to 2 decimal places)
Answer:
(4H + 2L = 12,001) x -2 14 (7,333) + 20 (3,334) = $169,342
(2H + 4L = 16,000) x 4 14 (7,333.66) + 20 (3,333.17) = $169,334.64
Shadow Price = $7.36
– 8H – 4L = – 24,002
8H+ 16L = 64,000
12L = 39,998
L = 3,333.17
H = 7,333.66However, I can’t come up to H=7,333.66.
Could you kindly provide assistance?Either there are typing errors in the book you are using, or you have not copied out the question correctly.
The question as you have typed it says that the profit maximising output is 7,333 units of H and 3,334 units of L.
However that is not possible because that level of output would be using more hours and more kgs than are available!!!If this question is from a past exam or is from the BPP Revision Kit, then tell me which question – I will then be able to check the wording myself 🙂
(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.)
Thanks John, I think indeed there may be something wrong with the question. The question is from a free revision package from vifhe (virtual institute for higher education). I think they are based in Pakistan.
And yes, I’ve watched and enjoyed all the lectures, including the revision lectures.
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