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It costs a certain bicycle factory a fixed amount of $11,000 to operat

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It costs a certain bicycle factory a fixed amount of $11,000 to operat  [#permalink]

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New post 09 Jun 2018, 00:08
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It costs a certain bicycle factory a fixed amount of $11,000 to operate for one month, plus $300 for each bicycle produced during the month. Each of the bicycles sells for a retail price of $700. What is the minimum number of bicycles that the factory must sell in one month to make a profit?

(A) 26
(B) 27
(C) 28
(D) 29
(E) 30

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Re: It costs a certain bicycle factory a fixed amount of $11,000 to operat  [#permalink]

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New post 09 Jun 2018, 01:31
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Bunuel wrote:
It costs a certain bicycle factory a fixed amount of $11,000 to operate for one month, plus $300 for each bicycle produced during the month. Each of the bicycles sells for a retail price of $700. What is the minimum number of bicycles that the factory must sell in one month to make a profit?

(A) 26
(B) 27
(C) 28
(D) 29
(E) 30


Let, after x cycles produced and sold will cause some profit

Total revenue = 700x

Total Cost = 11000+300x

For Profit, Revenue > Cost

i.e. 700x > 11000 + 300x

i.e. 400x > 11000

i.e. x > 27.5

i.e. x = 28 for minimum value of x

Answer: option C
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Re: It costs a certain bicycle factory a fixed amount of $11,000 to operat  [#permalink]

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New post 09 Jun 2018, 03:52
Bunuel wrote:
It costs a certain bicycle factory a fixed amount of $11,000 to operate for one month, plus $300 for each bicycle produced during the month. Each of the bicycles sells for a retail price of $700. What is the minimum number of bicycles that the factory must sell in one month to make a profit?

(A) 26
(B) 27
(C) 28
(D) 29
(E) 30


As the calculation we're asked to do is relatively straightforward, we'll just do it.
This is a Precise approach.

If each bicycle costs $300 and sells for $700, the profit per bicycle is $400.
So:
400x > 11,000
4x > 110
2x > 55
x > 27.5

(C) is our answer.
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It costs a certain bicycle factory a fixed amount of $11,000 to operat  [#permalink]

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New post 09 Jun 2018, 08:41
Bunuel wrote:
It costs a certain bicycle factory a fixed amount of $11,000 to operate for one month, plus $300 for each bicycle produced during the month. Each of the bicycles sells for a retail price of $700. What is the minimum number of bicycles that the factory must sell in one month to make a profit?

(A) 26
(B) 27
(C) 28
(D) 29
(E) 30


Given Total cost incurred per cycle per month = operating cost+production cost=11000+300*1
Total cost incurred towards 'n' nos of cycles per month=(11000+300n)$
Given selling price per cycle=700$
So, Selling price of 'n' nos of cycles=700n$
in order to make profit,\((Selling price of 'n' nos of cycles-Total cost of 'n' nos of cycles per month)>0\)
Or, 700n-(11000+300n)>0
Or, n>27.5
Therefore, minimum value of n is 28.

Ans. C
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Re: It costs a certain bicycle factory a fixed amount of $11,000 to operat  [#permalink]

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New post 10 Jun 2018, 04:29
As per the others, it's 400x > 11000, and thus x > 11000/400 (because x is positive). The reasoning is because the total revenue must be greater than total costs.

So 700x > 300x + 11000. Since x is positive, we can simplify that to 700x - 300x > 11000; i.e. 400x > 11000 as above.
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Re: It costs a certain bicycle factory a fixed amount of $11,000 to operat  [#permalink]

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New post 27 Mar 2019, 10:47
Bunuel wrote:
It costs a certain bicycle factory a fixed amount of $11,000 to operate for one month, plus $300 for each bicycle produced during the month. Each of the bicycles sells for a retail price of $700. What is the minimum number of bicycles that the factory must sell in one month to make a profit?

(A) 26
(B) 27
(C) 28
(D) 29
(E) 30


equate given info
11000+300n-700n=0 ' this shall be break even point where expense = revenue"
so
solve for n
we get
n=27.5 ~ 28
IMO C
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Re: It costs a certain bicycle factory a fixed amount of $11,000 to operat  [#permalink]

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New post 02 Apr 2019, 19:07
Bunuel wrote:
It costs a certain bicycle factory a fixed amount of $11,000 to operate for one month, plus $300 for each bicycle produced during the month. Each of the bicycles sells for a retail price of $700. What is the minimum number of bicycles that the factory must sell in one month to make a profit?

(A) 26
(B) 27
(C) 28
(D) 29
(E) 30


We can create the following inequality:

700n > 11,000 + 300n

400n > 11,000

n = 11,000/400 = 110/4 = 55/2 = 27.5

So 28 bicycles must be produced.

Answer: C
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Re: It costs a certain bicycle factory a fixed amount of $11,000 to operat   [#permalink] 02 Apr 2019, 19:07
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