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Q plc makes two products – Quone and Qutwo – from the same raw material. The selling
price and cost details of these products are as shown below:
Quone Qutwo
$ $
Selling price 20.00 18.00
Direct material ($2.00 per kg) 6.00 5.00
Direct labour 4.00 3.00
Variable overhead 2.00 1.50
––––– –––––
12.00 9.50
––––– –––––
Contribution per unit 8.00 8.50
The maximum demand for these products is 500 units per week for Quone, and an
unlimited number of units per week for Qutwo
.
What is the shadow price of these materials, if material were limited to 2,000 kg per
week? Pick from list
List options are:
• $nil
• $2.00 per kg
• $2.66 per kg
• $3.40 per kgi have watched the lecture on this topic
i don’t know how they got 2.5 kg in the the answerAnswer
$8.50/2.5 kg = $3.40 this is the shadow priceI don’t know which lecture you watched, but this question is testing on two lectures – the lecture on linear programming which is where I explain what is meant by the shadow price, and the lecture on key factor analysis (because there is only one constraint).
Quone is using $6/$2 = 3 kg of the material. Qutwo is using $5/$2 = 2.5 kg of the material.
Therefore Quone is generating a contribution of $8/3 = $2.67 per kg, and Qutwo is generating a contribution of $8.50/2.5 = $3.4 per kg.
Therefore currently they will use all of the material making Qutwo.
If they get 1 more kg of the material then they will use it to make more Qutwo’s (because it has the higher contribution per kg.). As a result the contribution will increase by $3.40 and this is therefore the shadow price of the material.
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