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ABC Car Company wants to manufacture a new car known a

by vinni.k » Fri Oct 13, 2017 12:16 pm
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

OA is C

I have an official solution, it has a very long explanation, and i also did exactly the same way. Can you please tell any shorter approach ?
profit = revenue - expenses
30,500,000 = 20,000s - (5,000(20,000) + 50,200,000)

Thanks
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by Jay@ManhattanReview » Fri Oct 13, 2017 11:10 pm
vinni.k wrote: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

OA is C

I have an official solution, it has a very long explanation, and i also did exactly the same way. Can you please tell any shorter approach ?
profit = revenue - expenses
30,500,000 = 20,000s - (5,000(20,000) + 50,200,000)

Thanks
I think the official solution is an efficient one. Yes, you will have to deal with many 0s, but's okay; many of them would cancel. Let's see how.

We have

30,500,000 = 20,000s - (5,000(20,000) + 50,200,000)

We can cancel four 0s from the LHS and the RHS

Thus, we get 3050 = 2s - (5000(2) + 5020)

3050 = 2s - (10000 + 5020)

3050 = 2s - 15020

2s = 15020 + 3050 = 18070

=> s = $9035

The correct answer: C

Hope this helps!

-Jay

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by vinni.k » Sat Oct 14, 2017 11:28 am
Thanks Jay :D
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by [email protected] » Sat Oct 14, 2017 11:30 am
Hi vinni.k,

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: C

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Re: ABC Car Company wants to manufacture a new car known a

by Scott@TargetTestPrep » Thu Jan 23, 2020 9:18 am
vinni.k wrote: ↑
Fri Oct 13, 2017 12:16 pm
 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

OA is C

I have an official solution, it has a very long explanation, and i also did exactly the same way. Can you please tell any shorter approach ?
profit = revenue - expenses
30,500,000 = 20,000s - (5,000(20,000) + 50,200,000)

Thanks
Let x = the selling price of a Model X car. Since revenue - cost = profit, we have:

20,000x - [20,000(5,000) + 50,200,000] = 30,500,000

20,000x - 150,200,000 = 30,500,000

20,000x = 180,700,000

x = 9,035

Answer: C

Scott Woodbury-Stewart
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[email protected]

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