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ABC Car Company wants to manufacture a new car known as Model X, and i

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ABC Car Company wants to manufacture a new car known as Model X, and i [#permalink]

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New post 05 Jan 2015, 06:57
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  35% (medium)

Question Stats:

80% (02:31) correct 20% (02:35) wrong based on 139 sessions

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Tough and Tricky questions: Word Problems.



ABC Car Company wants to manufacture a new car known as Model X, and it is trying to determine how many cars it needs to sell in order to make an annual profit of $30,500,000. The annual fixed costs for Model X total $50,200,000. In addition, each Model X car has an average cost of $5,000 per vehicle to manufacture. If the Company forecasts it will sell 20,000 Model X cars this year, at what price must the Company sell the car to achieve the desired annual profit?

A. $4,035
B. $4,036
C. $9,035
D. $16,140
E. $36,140

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Re: ABC Car Company wants to manufacture a new car known as Model X, and i [#permalink]

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New post 05 Jan 2015, 08:03
1
The company plans to make a profit of $30,500,000 and it needs to earn the fixed costs of $50,200,000, so it needs to earn $80,700,000 on top of the costs for the production of the 20,000 cars.

Therefore, price of each car needs to be the unit costs plus $80,700,000/20,000. After removing the 0's, we end with the unit costs plus $8,070/2, which is $5,000 plus $4,035. Therefore, Answer C is correct.
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Re: ABC Car Company wants to manufacture a new car known as Model X, and i [#permalink]

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New post 05 Jan 2015, 17:23
Bunuel wrote:

Tough and Tricky questions: Word Problems.



ABC Car Company wants to manufacture a new car known as Model X, and it is trying to determine how many cars it needs to sell in order to make an annual profit of $30,500,000. The annual fixed costs for Model X total $50,200,000. In addition, each Model X car has an average cost of $5,000 per vehicle to manufacture. If the Company forecasts it will sell 20,000 Model X cars this year, at what price must the Company sell the car to achieve the desired annual profit?

A. $4,035
B. $4,036
C. $9,035
D. $16,140
E. $36,140

Kudos for a correct solution.



Total Manufacturing cost = 20000 * 5000 = 100,000,000
Total cost to the company to make model x = Manufacturing cost + Fixed cost = 150,200,000
Expected revenue = Expenditure + profit expected = 150,200,000+30,500,000 = 180,200,000

Cost of each car = 180,200,000/20000 = 9,035

Ans C
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Re: ABC Car Company wants to manufacture a new car known as Model X, and i [#permalink]

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New post 05 Jan 2015, 23:39
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Answer = C. $9,035

Profit required per vehicle \(= \frac{30,500,000}{20000} = 1525\)

Fix cost per vehicle \(= \frac{50,200,000}{20000} = 2510\)

Cost price per vehicle = 5000

Total selling price = 5000+2510+1525 = 9035
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Re: ABC Car Company wants to manufacture a new car known as Model X, and i [#permalink]

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New post 09 Jan 2015, 07:21
Bunuel wrote:

Tough and Tricky questions: Word Problems.



ABC Car Company wants to manufacture a new car known as Model X, and it is trying to determine how many cars it needs to sell in order to make an annual profit of $30,500,000. The annual fixed costs for Model X total $50,200,000. In addition, each Model X car has an average cost of $5,000 per vehicle to manufacture. If the Company forecasts it will sell 20,000 Model X cars this year, at what price must the Company sell the car to achieve the desired annual profit?

A. $4,035
B. $4,036
C. $9,035
D. $16,140
E. $36,140

Kudos for a correct solution.


OFFICIAL SOLUTION:

(C) For this problem, we will use the formula: profit = revenue – expenses.

It may be easiest to begin labeling the variables to determine what it is we are missing.

Profit = $30,500,000
Expected quantity of Model X cars sold = 20,000
Expenses: = variable costs(quantity sold) + fixed costs = 5,000(20,000) + 50,200,000
Selling price of Model X = s
Revenue: = quantity sold × selling price = 20,000s

Now we can insert the known values into the formula: profit = revenue – expenses to solve for the answer.
30,500,000 = 20,000s – (5,000(20,000) + 50,200,000)
30,500,000 = 20,000s – (100,000,000 + 50,200,000)
30,500,000 = 20,000s – (150,200,000)
30,500,000+150,200,000 = 20,000s
180,700,000 = 20,000s
s = $9,035
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Re: ABC Car Company wants to manufacture a new car known as Model X, and i [#permalink]

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New post 02 Jul 2017, 10:22
Well, the way i did was somehow different. I subtracted the fixed cost per unit from the variable cost per unit right in the formula and then subtracted the overhead cost and equaled every thing to the profit.

Let the price per unit be \(x\)

\(20,000 (x-5,000) - 50,200,000=30,500,000 => 20,000X - 100,000,000 -50,200,000=30,500,00\)

We can reduce the zeros in order to make calculation easy. Therefore, i am going to drop 4 Zeros.

\(2X=10000 + 5020 + 3050 => 2X= 18070 => X = \frac{18070}{2} = 9035\)
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Re: ABC Car Company wants to manufacture a new car known as Model X, and i [#permalink]

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New post 05 Jan 2018, 17:17
Hi All,

The answer choices are 'spread out' enough that you can use estimation to answer this question (although you will still have to be careful to keep track of the digits involved).

Our 'goal' is to have a PROFIT of approximately $30,000,000. We know that there are FIXED COSTS of approximately $50,000,000, so with just these two values, we would need REVENUE of approximately:
$30,000,000 + $50,000,000 = $80,000,000

However, we also have to consider the manufacturing COST per vehicle ($5,000 per vehicle for 20,000 vehicles). That would be:
($5,000)(20,000) = $100,000,000

Thus, we need TOTAL REVENUE to be:
$80,000,000 + $100,000,000 = $180,000,000

To hit that total, the price that we sell each car for would have to be approximately:
$180,000,000/20,000 =
$180,000/20 =
$9,000 approximately

Final Answer:

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Re: ABC Car Company wants to manufacture a new car known as Model X, and i   [#permalink] 05 Jan 2018, 17:17
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