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Hi,
There are two questions for which I don’t understand the answer. They are taken from Kaplan exam kit 17/18.Q.66
Two products Q1 and Q2 are made from the same raw material.
Selling price $20 and $18
Direct material ($2/kilo) $6 and $5
Direct labour $4 and $3
Variable o/h $2 and $1.50
Contribution/unit $8 and $8.50The max demand for these products is 500 units per week for Q1 and unlimited for Q2.
What would the shadow price of these materials be if material were limited to 2,000 kgs per week?
A Nil
B $2/kg
C $2.66/kg
D $3.40/kiloThe book says that answer is D because $8.50/2.5kg=$3.40.
But how can that be the shadow price? Why is it only calculated on Q2 figures? I understood that the shadow price is the difference between the contribution at the level of resources we have and at the level of resources we would have adding one more unit of resource. Contribution per unit/limited factor should just give me the relation to then rank the products, how can that be the shadow price? I can’t even make the whole calculation with the equations here, so I thought that the shadow price could not be calculated.Q.67
P is considering whether to continue making a component or to buy it from an outside supplier. It uses 12,000 of the components each year. The internal manufacturing cost comprises:
Direct materials $3/unit
Direct labour $4/unit
Variable o/h $1/unit
Specific fixed cost $2.5/unit
Other fixed costs $2/unitIf the direct labour were not used to manufacture the component, it would be used to increase the production of another item for which there is unlimited demand. This other item has a contribution of $10 per unit but requires $8 of labour per unit.
What is the maximum price per component, at which buying is preferable to internal manufacture?
A $8
B $10.50
C $12.50
D $15.50The book says the answer is D and their calculation is:
Direct materials $3
Direct labour $9 ($10/2+$4)
Variable o/h $1
Specific fixed cost $2.5
No other fixed costsI don’t understand at all the calculation they made, especially the one for direct labour. Why is the contribution divided by 2?
Thanks a lot!
Q66 The contribution per kg is 8/3 = $2.66 for Q1, and 8.5/2.5 = $3.40 for Q2. Therefore Q2 is best.
They have 2,000 kg of material and they will therefore use it all making 2,000/2.5 = 800 units of Q2.
If they have 1 more kg of material then they would use it to make more Q2 and therefore earn an extra $3.40. Therefore this is the shadow price.Q67 They have divided by 2 because since the other item required $8 of labour and the internal cost of the component is only $4 of labour, then the other item must be taking 2 times as much time to make.
Hello sir,
About qn 66, could I say that there is just one limiting factor and that Linear programming is not needed?Since demand is always used as a mere final allocation, it World not be counted as a constraint to the effect of needing LP.
is that it?
Linear programming is certainly not needed.
I am not sure what you mean by ‘demand always used as a mere final allocation’.
Had the maximum demand for Q2 been (say) 500 units, and the demand for Q1 had been unlimited, then they would have made Q2 in full and then made some Q1. So more material would have meant they would make more Q1 and the shadow price would be the contribution form Q1.
This is a normal key factor problem, not a linear programming problem.
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