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12 Jul 2021, 04:45
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
65% (03:33) correct
35%
(03:24)
wrong
based on 386
sessions
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A farmer has exactly 1,000 square feet of farmland, on which he can grow both soy and corn. Every square foot can produce either one pound of soy or three pounds of corn. If soy can be sold on the market for $12/pound for the first hundred pounds and then $6 per pound after that, and corn can be sold on the market for $10/pound, what is the number of square feet of farmland that the farmer should devote to soy to make a profit of exactly $13,080?
(A) 30
(B) 100
(C) 270
(D) 600
(E) 730
(A) 30
(B) 100
(C) 270
(D) 600
(E) 730
12 Jul 2021, 06:38
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Soluiton:
Assuming that there is no cost of production thus no CP.
let us assume the number of square feet that farmer will devote to soy be \(x\).
Amount of soy produced in this area \(= x\) pounds
So the number of square feet for corm \(= 1000-x\)
Amount of corm produced in this area \(= 3(1000-x)\) pounds
Now there can be 2 cases:
Case 1: When \(x > 100\)
In that case: SP of soy \(= 1200 + 6(x-100)\)
SP of corn \(= 30(1000-x)\)
So we can write: \(1200 + 6(x - 100) + 30 (1000 - x) = 13080\)
\(⇒ 1200+6x-600+30000-30x=13080\)
\(⇒ -24x = -17520\)
\(⇒ x = 730\)
Option E says 730. But let us check case 2 as well.
Case 2: When \(x<=100\)
In this case we can say: \(12x + 30(1000 -x) = 13080\)
Solvinf which we get \(x = 940\) (which is not possible as \(x<=100\))
Hence the right answer is Option E.
Assuming that there is no cost of production thus no CP.
let us assume the number of square feet that farmer will devote to soy be \(x\).
Amount of soy produced in this area \(= x\) pounds
So the number of square feet for corm \(= 1000-x\)
Amount of corm produced in this area \(= 3(1000-x)\) pounds
Now there can be 2 cases:
Case 1: When \(x > 100\)
In that case: SP of soy \(= 1200 + 6(x-100)\)
SP of corn \(= 30(1000-x)\)
So we can write: \(1200 + 6(x - 100) + 30 (1000 - x) = 13080\)
\(⇒ 1200+6x-600+30000-30x=13080\)
\(⇒ -24x = -17520\)
\(⇒ x = 730\)
Option E says 730. But let us check case 2 as well.
Case 2: When \(x<=100\)
In this case we can say: \(12x + 30(1000 -x) = 13080\)
Solvinf which we get \(x = 940\) (which is not possible as \(x<=100\))
Hence the right answer is Option E.
12 Jul 2021, 06:54
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Bunuel
We'd need to know about expenses to answer a "profit" question, so this should be asking about revenue. It's also a bit of a mystery why anyone would want to make that specific amount of profit. Anyway, for corn this farmer is making $30 per square foot (3 pounds per square foot at $10/pound). So if this farmer devoted half of his land to corn, and did nothing at all with the other half, he'd make $15 per square foot, and $15,000 in profit. That's way too high, so he must be devoting less than half his land to corn, and more than half to soy, and only D or E could be right. But it's very quick to rule out D also: that would mean 400 square feet of corn, and $12,000 in corn revenue, plus more than 6(600) = $3600 in soy revenue (since the 600 square feet of soy make at least $6 per square foot) which is again way too high. So E must be the answer, and if we really wanted to confirm that, we could, but that doesn't seem like it would be all that pleasant considering how complicated the setup is.
