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A firm has two production choices. It could sell Q3 posters at a price

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A firm has two production choices. It could sell Q3 posters at a price  [#permalink]

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New post 11 Nov 2019, 04:10
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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


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Re: A firm has two production choices. It could sell Q3 posters at a price  [#permalink]

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New post 13 Nov 2019, 23:57
Bunuel 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


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It could sell Q3 posters at a price of $3 each. If it does this, its total cost of production will be C3 dollars...\(P_3=3Q_3-C_3\)
, the firm could sell Q5 posters at $5 each, with a total cost of C5 dollars .......\(P_5=5Q_5-C_5\)
We have to compare P_3 and P_5

(1) Q3 is twice Q5 and C3 is twice C5.
\(P_3=3Q_3-C_3=3(2P_5)-2C_5=6P_5-2C_5\) and \(P_5=5Q_5-C_5\)
so \(P_3-P_5=6P_5-2C_5-(5Q_5-C_5)=Q_5-C_5\)...
From \(Q_3 > Q_5 > C_3 > C_5 > 0.....Q_5-C_5>0\), so \(P_3-P_5>0....P_3>P_5\)
Suff

(2) Q5 = 6000 and C5 = $2518
Nothing much as we do not know other values..
\(P_5=5Q_5-C_5=5*6000-2518=30000-2518=27482\)..
\(Q_3 > Q_5 > C_3 > C_5 > 0.....\)...\(Q_3 > 6000 > C_3 > 2518 > 0....\)
Various possibilities...
(1) \(20000> 6000 > 4000 > 2518 > 0....\)......\(P_5=3*20000-4000=56000>27482\)
(2) \(7000> 6000 > 4000 > 2518 > 0....\)......\(P_5=3*7000-4000=17000<27482\)
Insuff

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Re: A firm has two production choices. It could sell Q3 posters at a price   [#permalink] 13 Nov 2019, 23:57
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