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two production choices

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by vk_vinayak » Tue Aug 21, 2012 3:00 am
A firm has two production choices. It could sell Q3 posters at a price of $3 each. If it does this, its total cost of production will be C3 dollars. Alternately, the firm could sell Q5 posters at $5 each, with a total cost of C5 dollars and where Q3 > Q5 > C3 > C5 > 0. Which decision will give the firm a larger profit, if profits are defined as total sales income minus total costs?

(1) Q3 is twice Q5 and C3 is twice C5.

(2) Q5 = 6000 and C5 = $2518

I somehow guessed it halfway through equations. Details would be helpful.
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Source: — Data Sufficiency |
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by anuprajan5 » Tue Aug 21, 2012 4:28 am
Vinayak,

I have a skewered logic around this but would the answer be A

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by SmartAssJun » Wed Aug 22, 2012 6:36 pm
vk_vinayak wrote:A firm has two production choices. It could sell Q3 posters at a price of $3 each. If it does this, its total cost of production will be C3 dollars. Alternately, the firm could sell Q5 posters at $5 each, with a total cost of C5 dollars and where Q3 > Q5 > C3 > C5 > 0. Which decision will give the firm a larger profit, if profits are defined as total sales income minus total costs?

(1) Q3 is twice Q5 and C3 is twice C5.

(2) Q5 = 6000 and C5 = $2518

I somehow guessed it halfway through equations. Details would be helpful.
First, let's say the profit you make out of Q3 posters sold would be: 3Q3-C3
and if you sell Q5 of them, it would be: 5Q5-C5

Statement 1:
Q3 is twice Q5 and C3 is twice C5.
This means ==> 3Q3-C3= 6Q5-2C5
We can tell that 6Q5-2C5-(5Q5-C5)=Q5-C5, and Q5>C5. Therefore you can see
that selling Q3 posters is more profitable. So statement 1 alone is sufficient.

Statement 2: is clearly insufficient because you have no idea how much larger
Q3 is than Q5 or how much larger C3 is than C3.
So the correct answer is A
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