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

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Math Expert
Joined: 02 Sep 2009
Posts: 60515
A firm has two production choices. It could sell Q3 posters at a price  [#permalink]

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11 Nov 2019, 04:10
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57% (02:54) correct 43% (01:37) wrong based on 7 sessions

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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 Are You Up For the Challenge: 700 Level Questions _________________ Math Expert Joined: 02 Aug 2009 Posts: 8344 Re: A firm has two production choices. It could sell Q3 posters at a price [#permalink] ### Show Tags 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

Are You Up For the Challenge: 700 Level Questions

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

A
_________________
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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