Problem Solving

Hi Vincen,

While this question is a bit 'wordy', there's a great built-in logic 'shortcut' that you can use to minimize the amount of work that you need to do to get to the correct answer. To start, we're given a couple of facts to work with:
1) There are 600 units produced and sold
2) Each unit COST $90 to make

We're asked for the price at which the TOTAL PROFIT from the sale of these units = $42,000.

Since there are 600 units, then each unit has to bring in $42,000/600 = $70 in profit. The COST of each unit is $90, so to hit that total profit, we just need to increase that $90 by $70 on each unit.

$90 + $70 = $160

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Vincen wrote:A television manufacturer produces 600 units of a certain model each month at a cost to the manufacturer of $90 per unit and all of the produced units are sold each month. What is the minimum selling price per unit that will ensure that the monthly profit (revenue from sales minus the manufacturer's cost to produce) on the sales of these units will be at least $42,000?

A) $110
B) $120
C) $140
D) $160
E) $180

The OA is D.

Should I find the cost function? How can I solve this PS question?

We are given that

Monthly Profit = Revenue from sales - Cost to produce

Or,

Monthly Profit on 600 units = Revenue from sales of 600 units - Cost of 600 units

42000 = Revenue from sales of 600 units - 600 x 90

=> Revenue from sales of 600 units = 42000 + 54000 = 96000

Revenue from sales of one unit (Selling price per unit) = 96000 / 600 = $160.

The correct answer: D

Hope this helps!

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Vincen wrote:A television manufacturer produces 600 units of a certain model each month at a cost to the manufacturer of $90 per unit and all of the produced units are sold each month. What is the minimum selling price per unit that will ensure that the monthly profit (revenue from sales minus the manufacturer's cost to produce) on the sales of these units will be at least $42,000?

A) $110
B) $120
C) $140
D) $160
E) $180

The OA is D.

We can let p = the selling price per unit and create the following equation:

600p - 600(90) ≥ 42,000

600p - 54,000 ≥ 42,000

600p ≥ 96,000

p ≥ 160

Since p ≥ 160, we see that the minimum selling price must be $160.

Answer: D