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

by AAPL » Mon Mar 19, 2018 6:27 am
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 (revenue from sales minus production costs) will be at least $626,400?

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

The OA is A.

I solved this PS question as follow,

We need to set up an equation.

450*12(x-110)=626400

Where x is a selling cost of one item

x-110, is a profit from one item

450 - number of items produced and sold per month

12 - is a number of month in a year

Simplifying the equation will lead to x - 110 = 116, then x = 226.

Is there another strategic approach to solve this PS question? Can any experts help, please? Thanks!
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by [email protected] » Mon Mar 19, 2018 2:41 pm
Hi AAPL,

We're told that 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. We're asked for the MINIMUM selling price per component that will guarantee that the YEARLY profit (revenue from sales minus production costs) will be at least $626,400. Since we're given all of the necessary numbers to work with, the speed with which you answer this question will come down to how you choose to do the 'math.'

With 450 units produced each month, we will end up with (12)(450) = 5400 units produced each year

For the profit to be AT LEAST $626,400, we need to divide by 5400 and then add back the production cost per unit ($110 each):

626,400/5400 =
6264/54 =
$116 of profit per unit

Factoring back the original cost per unit, we have a minimum selling price of 116 + 110 = $226 per unit

Final Answer: A

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by Jeff@TargetTestPrep » Wed Mar 21, 2018 3:24 pm
AAPL 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 (revenue from sales minus production costs) will be at least $626,400?

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

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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