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Hello,
Following is question 100 from the Kaplan exam kit.
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 the material were limited to 2,000 kgs per
week? Pick from list
List options are:
• $nil
• $2.00 per kg
• $2.66 per kg
• $3.40 per kgSir, can you please help me understand what the question is asking here and how to solve it?
I saw the answer in the book but I didn’t quite get it.Given that there is only one limited resource in that materials are limited to 2,000 kg, you use standard key factor analysis (contribution per kg of material) to rank so as to decide which of the two products is best. You will then make 500 of the best one (because that is the most that can be sold) and use the rest of the 2,000 kg on the other one.
Obviously if more kg were available you would then make more of the second best unit, and the shadow cost, as per the standard definition, is the most extra that you would be prepared to pay for one extra kg of material, which is equal to the contribution per kg generated from the second best product (which you would already have calculated in the first step of this).
okay, so you’re saying that contribution would be 2.67 (8/3) for A and 3.4 (8.5/2.5) for B.
So, product B is the best.and shadow price would also be 3.4. that is fine.
but I don’t quite understand what do you mean by “You will then make 500 of the best one (because that is the most that can be sold) and use the rest of the 2,000 kg on the other one.
Why would we make only 500 units of the best one (i.e. Qutwo)? I mean it has an unlimited demand.
Sorry, the answer should be 3.40.
I was reading too fast and thinking that demand was limited to 500 for each of the two products (in which case what I wrote would have been correct).
However, as you have written, since the demand for Qutwo is unlimited it would be more Qutwo that would be made which would make the shadow price equal to 3.40 per kg.
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