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Firm A's revenues are described by the equation Ra = 17.12x

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bhandariavi
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Firm A's revenues are described by the equation Ra = 17.12x [#permalink] New post   30 Jan 2011, 17:49
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Firm A's revenues are described by the equation Ra = 17.12x and its costs by Ca = 12.87x + 2400.
Firm B's revenues are described by the equation Rb = 13.27x and its costs by Cb = 8.77x + 1500.

(x denotes the quantity of sales).

If A's volume of sales increases from 1000 to 2000 over the same period that B's volume increases from 2000 to 3000, the percent increase in profits for the firm with the biggest dollar increase in profits is

A. 20%
B. 30%
C. 60%
D. 50%
E. 33%
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e1s
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Re: Problem solving--need the short cut way to answer this [#permalink] New post   31 Jan 2011, 03:29
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Ok, I do not know whether it is exactly what you want to hear but I did it that way: first look at difference between revenue and variable cost => take the bigger one (b) which gives you: 4.5x-1500 just plug in 2000 and 3000. you get 7500 and 12000 (difference 4500). 4500> 0.5*7500 so 60%

took me less than 1 minute, so I do not know whether there is actually a shorter way
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bhandariavi
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Re: Problem solving--need the short cut way to answer this [#permalink] New post   31 Jan 2011, 05:50
this one looks great approach. Thanks!
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Re: Problem solving--need the short cut way to answer this [#permalink] New post   31 Jan 2011, 20:25
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bhandariavi wrote:
:oops: Firm A's revenues are described by the equation Ra = 17.12x and its costs by Ca = 12.87x + 2400.

Firm B's revenues are described by the equation Rb = 13.27x and its costs by Cb = 8.77x + 1500.

(x denotes the quantity of sales).
If A's volume of sales increases from 1000 to 2000 over the same period that B's volume increases from 2000 to 3000, the percent increase in profits for the firm with the biggest dollar increase in profits is

1) 20% 2)30% 3) 60% 4)50% 5)33%

I can calculate the answer But i need the short cut way to do this.
Testluv, Bunuel, Pkit, shrouded1, icandynyone or anyone who can solve this with short cut approach ----Help me!!!!!!


We need to compare profits so find out profit in the two cases:
A: 17.12x - (12.87x + 2400) = 4.25x - 2400
B: 13.27x - (8.77x + 1500) = 4.5x - 1500
In both cases, x changes by 1000 so B will give a higher dollar increase (because 4.5 > 4.25)
% increase in B's profit: \(\frac{4.5*1000}{{4.5*2000 - 1500}} * 100 = 60%\)
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Re: Firm A's revenues are described by the equation Ra = 17.12x [#permalink] New post   21 May 2013, 01:19
VeritasPrepKarishma wrote:
We need to compare profits so find out profit in the two cases:
A: 17.12x - (12.87x + 2400) = 4.25x - 2400
B: 13.27x - (8.77x + 1500) = 4.5x - 1500
In both cases, x changes by 1000 so B will give a higher dollar increase (because 4.5 > 4.25)
% increase in B's profit:


why is it 2000 in the denominator?
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Re: Firm A's revenues are described by the equation Ra = 17.12x [#permalink] New post   21 May 2013, 03:57
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fozzzy wrote:
VeritasPrepKarishma wrote:
We need to compare profits so find out profit in the two cases:
A: 17.12x - (12.87x + 2400) = 4.25x - 2400
B: 13.27x - (8.77x + 1500) = 4.5x - 1500
In both cases, x changes by 1000 so B will give a higher dollar increase (because 4.5 > 4.25)
% increase in B's profit:


why is it 2000 in the denominator?



Because you need the % increase in profit.
The increase in profit = 4.5 * 1000 (increase in the units from 2000 to 3000)
The original profit = 4.5*2000 - 1500 (initially 2000 units were sold)

% increase = (4.5 * 1000)/(4.5*2000 - 1500) * 100
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Re: Firm A's revenues are described by the equation Ra = 17.12x [#permalink] New post   19 Apr 2024, 05:24
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Re: Firm A's revenues are described by the equation Ra = 17.12x [#permalink]
19 Apr 2024, 05:24
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