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A manufacturer produces items for which the production costs consists

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A manufacturer produces items for which the production costs consists [#permalink]

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New post 08 Jan 2018, 22:42
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A manufacturer produces items for which the production costs consists of annual fixed costs totaling $9,500 and variable costs averaging $10 per item. If the total cost to produce 50 items increases by 10 percent while the annual fixed cost stays the same, what is the new variable cost per item?

A. $10
B. $11
C. $20
D. $30
E. $50
[Reveal] Spoiler: OA

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Re: A manufacturer produces items for which the production costs consists [#permalink]

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New post 09 Jan 2018, 09:39
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Bunuel wrote:
A manufacturer produces items for which the production costs consists of annual fixed costs totaling $9,500 and variable costs averaging $10 per item. If the total cost to produce 50 items increases by 10 percent while the annual fixed cost stays the same, what is the new variable cost per item?

A. $10
B. $11
C. $20
D. $30
E. $50



Fixed costs: 9500$
Variable costs : 10$ per item

If total cost for 50 items increases by 10%,
the cost will be \(1.1(9500 + 10*50) = 1.1(10000) = 11000\)

New variable cost per item will be \(\frac{11000 - 9500}{50} = \frac{1500}{50}\) = $30(Option D)
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Re: A manufacturer produces items for which the production costs consists [#permalink]

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New post 09 Jan 2018, 09:40
Bunuel wrote:
A manufacturer produces items for which the production costs consists of annual fixed costs totaling $9,500 and variable costs averaging $10 per item. If the total cost to produce 50 items increases by 10 percent while the annual fixed cost stays the same, what is the new variable cost per item?

A. $10
B. $11
C. $20
D. $30
E. $50


9500+10*50=10000
10000+10%of 10000=10000+1000=11000

9500+50x=11000
X=30

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A manufacturer produces items for which the production costs consists [#permalink]

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New post 25 Jan 2018, 12:37
Bunuel wrote:
A manufacturer produces items for which the production costs consists of annual fixed costs totaling $9,500 and variable costs averaging $10 per item. If the total cost to produce 50 items increases by 10 percent while the annual fixed cost stays the same, what is the new variable cost per item?

A. $10
B. $11
C. $20
D. $30
E. $50

Variable cost = VC
Fixed Cost + (VC per item)*(# of items) = Total Cost

Total cost increases by 10 percent.

The trap answer is B. Answer B gives a VC per item calculated as if the original total did not include fixed cost of $9,500.

Easiest way, IMO, is to focus on total cost for two scenarios, original and increased (new).

1) Original total cost to produce 50 items:

Fixed Cost + (VC per item)(# of items) = Total Cost
$9,500 + ($10)(50) = Original Total Cost
($9,500 + $500) = $10,000 = Original Total Cost

2) Total cost increases by 10 percent
($10,000*1.1) = $11,000= New Total Cost

3) New VC per item
Same Fixed Cost + (VC\(_{new}\))(# of items)= New Total Cost

$9,500 + (VC per item)*(50 items) = $11,000

(VC per item)*(50 items) = ($11,000-$9,500)

(VC per item)*(50 items) = $1,500

VC per item = \(\frac{$1,500}{50items}= $30\)

Answer D
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Re: A manufacturer produces items for which the production costs consists [#permalink]

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New post 26 Jan 2018, 21:22
Bunuel wrote:
A manufacturer produces items for which the production costs consists of annual fixed costs totaling $9,500 and variable costs averaging $10 per item. If the total cost to produce 50 items increases by 10 percent while the annual fixed cost stays the same, what is the new variable cost per item?

A. $10
B. $11
C. $20
D. $30
E. $50


Let total cost be a and the new variable cost per item be b.

\(a = 9500 + 50(10) ----- 1\)
\(\frac{11a}{10} = 9500 + 50(b) --- 2\)

Divide Eqn 1 by 2, we get

\(b = 30\)
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Re: A manufacturer produces items for which the production costs consists   [#permalink] 26 Jan 2018, 21:22
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