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Hi,
I understand the approach on why we get 1.50 per hour of shadow price.
However for statement below, I need more clarification:
“This shadow price will cease to apply when the direct labour hours constraint is replaced in the optimal solution by the sales demand for Product Y constraint. At this level of output, total labour hours would be (10,000 units of X at 5 hours) + (12,000 units of Y at 4 hours) = 98,000 hours”
I know that with the product y constraint total labour hours is (10,000 x 5) + (2,500 x 4) = 60,000
but why when we are calculating the additional hours of labour?
1. The shadow price will cease to apply?
2. Why are we using 12,000 if shadow price will cease to apply?Quite confuse with this statement on why the answers is giving shadow price and additional hours in same sentence but it seems from explanation they are quite opposite , can help to explain and clarify please?
The shadow price will cease to apply when the direct labour hours constraint is replaced in the optimal solution by the sales demand for the Product Y constraint.
This means that once the company reaches the level of output where it is producing 10,000 units of Product X and 12,000 units of Product Y, the shadow price per direct labour hour will no longer be applicable.When calculating the additional hours of labour, we use 12,000 units of Product Y because it represents the maximum sales demand for Product Y.
The calculation takes into account the labour hours required to produce the maximum sales demand for both products, which is (10,000 units of X at 5 hours) + (12,000 units of Y at 4 hours) = 98,000 hours. This calculation helps determine the total labour hours required at the optimal level of output.The statement about the shadow price and additional hours in the same sentence may seem contradictory, but it refers to the fact that the shadow price per hour applies to the additional hours of labour beyond the current limit.
In this case, the shadow price per hour applies to the additional 38,000 hours of labour needed to reach the maximum sales demand for Product Y.
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