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WE:Corporate Finance (Venture Capital)
Re: An Opera house has 200 seats of two kinds: Box seats and Stall seats.
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09 Oct 2022, 21:39
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What we know
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Let b = the quantity of box seats available in the house
Let s = the quantity of stall seats available in the house
Now let b* = the actual quantity of box seats sold
And let s* = the actual quantity of stall seats sold
We know two things right away:
(1) We know b + s = 200
(2) We know 355b + 150s = 36,150
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What does A tell us?
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A says >85% of the seats of each type are sold.
So b* > 0.85 * b and s* > 0.85 * s
Let's take our statement from (2) above
355b + 150s = 36,150
0.85 * (355b + 150s) = 0.85 * 36,150
355(0.85)b + 150(0.85)s = 0.85 * 36,150
We know b* > 0.85b and s* > 0.85s, so we can say:
355b* + 150s* > 0.85*36,150 > 30,000
So A is sufficient!
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What does B tell us?
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The number of stall seats sold is approximately 5x the number of box seats. (What does approximately mean? No idea.)
But we can put it like this:
s* ~= 5b*
We can plug these in to estimate the actual sales with the following expression:
~355b* + 150(5b*)
~1,105b*
Now we know 355b + 150s = 36,150, which is a firm upper bound for the above.
So 1,105b* < 36,150 (roughly)
So b* < 33 (roughly)
Well, this isn't actually very useful information on its own.
Suppose b* = 1. Then the sales are roughly $1,105 -- this is far below $30,000.
But b* could also be about 30, in which case the sales are roughly $33,150, which is above $30,000
So part B doesn't actually tell us anything useful
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As a result, the answer is A