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A company produces 450 units of a particular computer...

by swerve » Mon Dec 18, 2017 3:12 pm
A company produces 450 units of a particular computer component every month, at a production cost to the company of $110 per component, and sells all of the components by the end of each month. What is the minimum selling price per component that will guarantee that the yearly profit (renueve from sales minus production cost) will be at least $626,400?

A. 226
B. 230
C. 240
D. 260
E. 280

The OA is A.

Please, can any expert explain this PS question for me? I don't understand why that is the correct answer. Thanks.
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by Jay@ManhattanReview » Tue Dec 19, 2017 1:36 am
swerve wrote:A company produces 450 units of a particular computer component every month, at a production cost to the company of $110 per component, and sells all of the components by the end of each month. What is the minimum selling price per component that will guarantee that the yearly profit (renueve from sales minus production cost) will be at least $626,400?

A. 226
B. 230
C. 240
D. 260
E. 280

The OA is A.

Please, can any expert explain this PS question for me? I don't understand why that is the correct answer. Thanks.
Say the seeling price of each component is $x, thus, total revenue = $450x

We have total cost = $450*110

Thus, yearly profit = 12[Revenue - Cost] = 12[450x - 450*110]

We are given that yearly profit must be at least $626,400, thus,

12[450x - 450*110] ≥ 626,400

x - 110 ≥ 626,400 / (12*450)

x - 110 ≥ 116

x ≥ 226

The correct answer: A

Hope this helps!

-Jay
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by GMATGuruNY » Tue Dec 19, 2017 5:48 am
swerve wrote:A company produces 450 units of a particular computer component every month, at a production cost to the company of $110 per component, and sells all of the components by the end of each month. What is the minimum selling price per component that will guarantee that the yearly profit (renueve from sales minus production cost) will be at least $626,400?

A. 226
B. 230
C. 240
D. 260
E. 280
Required monthly profit = (yearly profit)/(12 months) = (626,400)/12 = 52,200.
Required profit per unit = (required monthly profit)/(units sold each month) = (52,200)/450 = 116.
Required selling price = (cost price per unit) + (required profit per unit) = 110 + 116 = 226.

The correct answer is A.
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by Scott@TargetTestPrep » Fri Sep 13, 2019 3:26 pm
swerve wrote:A company produces 450 units of a particular computer component every month, at a production cost to the company of $110 per component, and sells all of the components by the end of each month. What is the minimum selling price per component that will guarantee that the yearly profit (renueve from sales minus production cost) will be at least $626,400?

A. 226
B. 230
C. 240
D. 260
E. 280

The OA is A.

Please, can any expert explain this PS question for me? I don't understand why that is the correct answer. Thanks.
Since $626,400 is the minimum annual profit, thus $626,400/12 = $52,200 will be the minimum monthly profit. We can let n = the minimum selling price and create the inequality:

450n - 110(450) ≥ 52,200

450n - 49,500 ≥ 52,200

450n ≥ 101,700

n ≥ 226

Answer: A

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