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The total cost for Company X to produce a batch of tools is

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The total cost for Company X to produce a batch of tools is  [#permalink]

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New post Updated on: 07 Apr 2012, 13:02
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The total cost for Company X to produce a batch of tools is $10,000 plus $3 per tool. Each tool sells for $8. The gross profit earned from producing and selling these tools is the total income from sales minus the total production cost. If a batch of 20,000 tools is produced and sold, then Company X’s gross profit per tool is

(A) $3.00
(B) $3.75
(C) $4.50
(D) $5.00
(E) $5.50

I keep getting an answer different from OA, and I know I must be missing something simple

Originally posted by terp26 on 25 Feb 2007, 21:50.
Last edited by Bunuel on 07 Apr 2012, 13:02, edited 2 times in total.
Edited the question and added the OA
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Re: The total cost for Company X to produce a batch of tools is  [#permalink]

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New post 07 Apr 2012, 13:07
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mymbadreamz wrote:
Can someone explain this please? thanks.


The total cost for Company X to produce a batch of tools is $10,000 plus $3 per tool. Each tool sells for $8. The gross profit earned from producing and selling these tools is the total income from sales minus the total production cost. If a batch of 20,000 tools is produced and sold, then Company X’s gross profit per tool is

(A) $3.00
(B) $3.75
(C) $4.50
(D) $5.00
(E) $5.50

The total production cost of 20,000 tools is $10,000 + $3*20,000 = $70,000;
The total income from sales of 20,000 tools is $8*20,000 = $160,000;

The gross profit earned is $160,000 - $70,000 = $90,000;
The gross profit per tool is $90,000/20,000 = $4.50.

Answer: C.

Hope it's clear.
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New post 26 Feb 2007, 02:13
I just did it real quickly and got 4.50.

Basically 90,000/20,000.
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New post 26 Feb 2007, 05:05
[(8-3)xno. of tools - 10.000]/no of tools is the answer which is
90,000/20,000=4.5
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New post 26 Feb 2007, 13:26
oh I see what I did wrong, I ended up with 170,000 - 70,000 meaning I incoroprated the 10,000 in the profits, when it was only part of the cost

Thanks
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New post 07 Apr 2012, 12:53
Can someone explain this please? thanks.
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Re: The total cost for Company X  [#permalink]

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New post 07 May 2012, 00:31
sravanth wrote:
The total cost for Company X to produce a batch of tools is $10,000 plus $3 per tool. Each tool sells for $8. The gross profit earned from producing and selling these tools is the total income from sales minus the total production cost. If a batch of 20,000 tools is produced and sold, then Company X’s gross profit per tool is

(A) $3.00
(B) $3.75
(C) $4.50
(D) $5.00
(E) $5.50


Merging similar topics. Please ask if anything remains unclear.
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Re: The total cost for Company X to produce a batch of tools is  [#permalink]

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New post 21 Jun 2012, 01:53
1
TC = 10,000 + 3x

TR = 8x

Profit = 8x - 10000 - 3x = 5x - 10000

when x = 20000, Profit = 90000

Profit per x = 90000/20000 = 4.5




terp26 wrote:
The total cost for Company X to produce a batch of tools is $10,000 plus $3 per tool. Each tool sells for $8. The gross profit earned from producing and selling these tools is the total income from sales minus the total production cost. If a batch of 20,000 tools is produced and sold, then Company X’s gross profit per tool is

(A) $3.00
(B) $3.75
(C) $4.50
(D) $5.00
(E) $5.50

I keep getting an answer different from OA, and I know I must be missing something simple
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Re: The total cost for Company X to produce a batch of tools is  [#permalink]

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New post 10 Jan 2014, 01:50
terp26 wrote:
The total cost for Company X to produce a batch of tools is $10,000 plus $3 per tool. Each tool sells for $8. The gross profit earned from producing and selling these tools is the total income from sales minus the total production cost. If a batch of 20,000 tools is produced and sold, then Company X’s gross profit per tool is

(A) $3.00
(B) $3.75
(C) $4.50
(D) $5.00
(E) $5.50

I keep getting an answer different from OA, and I know I must be missing something simple



Step 1) Create equations: [10,000 + 3*X = Total Cost] [5*X = Revenue] [Gross Profit = TC - R]

Step 2) Insert the variable: We are given X = 20,000 so Total cost = 70,000, Revenue = 160,000 and Gross Profit = 90,000

Now, the gross profit per tool is exactly what it says, Gross Profit/X ----> 90,000/20,000 ----> 4.5 USD per tool
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Re: The total cost for Company X to produce a batch of tools is  [#permalink]

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New post 11 Sep 2014, 06:43
terp26 wrote:
The total cost for Company X to produce a batch of tools is $10,000 plus $3 per tool. Each tool sells for $8. The gross profit earned from producing and selling these tools is the total income from sales minus the total production cost. If a batch of 20,000 tools is produced and sold, then Company X’s gross profit per tool is

(A) $3.00
(B) $3.75
(C) $4.50
(D) $5.00
(E) $5.50

I keep getting an answer different from OA, and I know I must be missing something simple



production cost = 10000 + (3*20000 ) = 70000

selling cost = 20000* 8 = 160000

160000-70000 = 90000/20000 = 4.5
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Re: The total cost for Company X to produce a batch of tools is  [#permalink]

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New post 11 Sep 2014, 08:02
This problem is simple but was hard for me at first. The way I ended up with a solution was seeing that each tool made $5 each and the 10,000 cost of production spread over 20,000 tools meant each tool had an additional cost of .50 making individual profit 4.50 per tool.
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Re: The total cost for Company X to produce a batch of tools is  [#permalink]

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New post 07 Jun 2016, 10:56
terp26 wrote:
The total cost for Company X to produce a batch of tools is $10,000 plus $3 per tool. Each tool sells for $8. The gross profit earned from producing and selling these tools is the total income from sales minus the total production cost. If a batch of 20,000 tools is produced and sold, then Company X’s gross profit per tool is

(A) $3.00
(B) $3.75
(C) $4.50
(D) $5.00
(E) $5.50


The problem first asks us to calculate the gross profit. The profit equation is as follows:

Profit = Revenue – Cost

In this particular case, we are given VARIABLE REVENUE and VARIABLE COST. This means that Company X makes a certain amount of revenue PER TOOL and has a certain cost PER TOOL. We also are given a FIXED COST. This is a cost that is constant and will not change. Thus we need to take into account the quantity of tools being produced and sold as well as the fixed cost. We can now generate a more detailed profit equation:

Profit = (number of tools sold)(revenue per tool) – [fixed cost + (number of tools made)(cost per tool)]

We are given the following:

fixed cost = $10,000

cost per tool = $3

revenue per tool = $8

Number of tools produced and sold = 20,000

We can now plug all this into our profit equation:

Profit = (number of tools sold)(revenue per tool) – [fixed cost + (number of tools made)(cost per tool)]

P = 20,000 x 8 – [10,000 + (3 x 20,000)]

P = 20,000 x 8 – [10,000 + (3 x 20,000)]

P = 160,000 – [10,000 + 60,000]

P = 160,000 – 70,000

P = 90,000

We have a profit of $90,000 for selling 20,000 tools, but remember that we need to determine the profit PER TOOL. To calculate this, we divide the total profit of $90,000 by the number of tools produced, which is 20,000. We have:

$90,000/20,000 = $9/2 = $4.50

Answer C.
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The total cost for Company X to produce a batch of tools is  [#permalink]

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New post 28 Jun 2016, 23:28
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terp26 wrote:
The total cost for Company X to produce a batch of tools is $10,000 plus $3 per tool. Each tool sells for $8. The gross profit earned from producing and selling these tools is the total income from sales minus the total production cost. If a batch of 20,000 tools is produced and sold, then Company X’s gross profit per tool is

(A) $3.00
(B) $3.75
(C) $4.50
(D) $5.00
(E) $5.50


Fixed cost = $10,000
Selling price is $8/tool and production cost is $3/tool.
$(8-3) = $5(Profit)

5*20,000 = $100,000
$100,000-$10,000(FC) = $90,000(Gross profit.)

Gross profit/tool = $90,000/20,000 = 4.5

C.
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Re: The total cost for Company X to produce a batch of tools is  [#permalink]

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New post 15 Nov 2016, 15:55
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We are trying to find out the profit per tool. Lets do this withou having to do a lot of math. Here is a simple way, we only divide once and the rest is given on the statement.

The statement tells us the selling of each tool $8.00 now we need to get the cost. We already know that each tool has a fixed cost of $3.00 and each batch is $10,000.

The only thing we actually need to do here is take allocate the $10,000 to each tool and then add it to the $3.00 cost per tool stated.

Lets divided the cost of the batch per tool: 20,000/ $10,000 = $0.50 per tool.

Voila! We have $8.00 - ($3.00 + $0.50) = $4.50
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New post 15 Jul 2017, 07:33
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Here's how this can be solved as well - If you prefer Algebra

Let n = Number of tools sold

Cost Price = 10,000 + 3n
Revenue = 8n
Gross profit = 8n - (10,000+3n) = 5n - 10,000

Gross Profit per tool = \(\frac{(5n-10,000)}{n}\) = \(5 - \frac{10,000}{n}\)

Plugging in given

Profit per tool = \(5 - \frac{10,000}{20,000} = 5 - \frac{1}{2} = 4.5\)

Answer Choice : C
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Re: The total cost for Company X to produce a batch of tools is  [#permalink]

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New post 19 Sep 2017, 23:24
another method,
for each tool making profit of $8 -$3 =$5(excluded with the initial cost of $10000)
for initial investment each tool cost is distributed with 10000/20000 = $0.5
so total profit = $5-$0.5 = $4.5
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Re: The total cost for Company X to produce a batch of tools is  [#permalink]

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New post 06 Sep 2018, 01:18
Since they have asked profit/unit, let us stick to that exactly and avoid big numbers.
Cost of production is 10,000 + 3$/unit
20,000 are produced and hence we can take cost of production as 10,000/20,000 + 3$/unit = 0.5 + 3 = 3.5$ / unit
Selling price is 8$ /unit
Hence profit = 8-3.5 = 4.5$/unit
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New post 16 Apr 2019, 11:24
Before jumping into the algebra, think. On questions such as this you can get to one possible answer by excluding the impossible. Doing less algebra saves you time and increases your accuracy.

Without the fixed cost of $10,000, the profit would be $5 a unit. Of course, with the fixed cost the profit will be less. So, eliminate answers D and E.

If you spread the fixed cost over a run of 10,000 units, the fixed cost would work out to $1 a unit, lowering the profit to $4 a unit. The run of 20,000 will reduce the fixed cost allocated to each unit, so the profit per unit must be greater than $4. Eliminate A and B.

Only C is possible.

Think before you algebra.
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Re: The total cost for Company X to produce a batch of tools is  [#permalink]

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New post 10 May 2019, 12:13
terp26 wrote:
The total cost for Company X to produce a batch of tools is $10,000 plus $3 per tool. Each tool sells for $8. The gross profit earned from producing and selling these tools is the total income from sales minus the total production cost. If a batch of 20,000 tools is produced and sold, then Company X’s gross profit per tool is

(A) $3.00
(B) $3.75
(C) $4.50
(D) $5.00
(E) $5.50

I keep getting an answer different from OA, and I know I must be missing something simple

Per unit sale =8
Per unit cost =3+10000/20000=3.5
So, profit per unit=8-3.5=4.5

Answer is C

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Re: The total cost for Company X to produce a batch of tools is  [#permalink]

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New post 08 Oct 2019, 09:58
Profit = Rev - Cost, we are asked P/n tools = ?
Easiest for me is to plug in and factor power of 10

\(P = (8*2*10^{4}) - (10^{4} + 3*2*10^{4})\)

\(P = 10^{4}*[(8*2*1) - (1 + 3*2*1)]\)

\(P = 10^{4}*[(16) - (7)]\)

\(P = 10^{4}*[9]\)

\(\frac{10^{4}*[9]}{2*10^{4}} = 4.5\)
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Re: The total cost for Company X to produce a batch of tools is   [#permalink] 08 Oct 2019, 09:58
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