[psychosamba]

Hi Chris,

Many thanks for your reply – it is much appreciated. What I had meant to say though in the initial question, was why not choose the optimal solution constraint of demand for y = 2,500 – particularly given a linear relationship exists with the demand for x for Direct Labour Hours?

Yet, when I choose y = 2,500, and therefore for 1 extra unit of direct labour hours:
5x + 4y = 60,001, I get x = 10,000.20

I then get a total value of contribution in this scenario of $95,001.60, which when set against the initial scenario, gives a shadow price of $1.60 – not $1.50.

Given a linear relationship exists between x & y for direct labour hours, I would have thought it was irrelevant whether x or y’s optimal demand amount is chosen for maximum contribution, as you would arrive at the same value for the shadow price of $1.50. But this is clearly not the case.

That is why I am confused. There seems to be some reasoning to choose the higher demand figure, that gives the higher contribution on it’s own – separate to y?

[Author]

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