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Hello,
Does anyone have the above book who could explain the final example on linear programming for me (Pg 100 part C). In part B it says it’s advisable to pay overtime to relax the constraints but in part C it mentions not relaxing the constraints – what does this mean and why in part B would it make 2.00 extra contribution but in part C the unit contribution is a loss?
Many Thanks
In part (a) labour is limited and this limits the number of units that can be produced.
If we get more labour (which is what relaxing the constraint means) then we can make more units and get more contribution. It is worth getting more labour (by paying overtime) if the extra contribution we get (by making more units) makes it worthwhile.
In part (c) it says that we cannot relax the constraints, which means that labour is still limited as it was in part (a). So we cannot make more units, and if we make the new product it limits what we can make of the others. It turns out that this would lose us money.
Many Thanks – sois is possible that we could get the labour and materials cheaper than the shadow price, dowe just have to assume that in the new P&L we just use the cost plus the shadow price but in reality the cost of labour and material and could be higher than the cost plus the shadow price?
Also what does the final statement mean – “Incorporating the contribution lost elsewhere by reallocating the scarce resources”?
There is no point comparing the actual price with the shadow price.
The shadow price is the most EXTRA that you would be prepared to pay for one extra unit of a limited resource.So, for example, suppose materials cost $10 per kg, but the supply was limited and you were using it all. The supplier offers you more, but will charge more for it. Well if the shadow price was $2 then it means that you would be prepared to pay up to $12 per kg for extra supplies.
I don’t have the Kaplan book and so I can’t explain the last statement out of context.
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