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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 kgs per
week?
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i didn’t get , the shadow price measure of how much they would be willing to pay to gain more of a scarce resource over and above the normal priceshouldn’t we add one extra KG to 2000 then i make equations and solve to get the quantity of Qutwo the the subtract it from the old quantity?
I think it’s Kaplan
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
If you are still unsure – Watch the lecture on linear programming which is where we explain what is meant by the shadow price
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