Question: 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?

1. $110
2. $120
3. $140
4. $160
5. $180

Correct Answer: D
Solution and Explanation:
Approach Solution 1:
The problem statement informs that:
Given:

• A television manufacturer produces 600 units of a certain model each month.
• He produces it at a cost to the manufacturer of $90 per unit.
• All of the produced units are sold each month.

Find Out:

• The minimum selling price per unit that will ensure that the monthly profit on the sales of these units will be at least $42,000.

The manufacturer produces 600 units each month and he produces at a cost of $90 per unit.
Therefore, total cost = 600 * 90 = $54000
Monthly profit on the sales of these units = $42000.
Therefore, total revenue per month = cost + profit = 54000 + 42000 = $96000
Hence, selling price per unit = 96000/600 = $160
Therefore, the minimum selling price per unit = $160

Approach Solution 2:
The problem statement implies that:
Given:

• A television manufacturer produces 600 units of a certain model each month.
• He produces it at a cost to the manufacturer of $90 per unit.
• All of the produced units are sold each month.

Find Out:

• The minimum selling price per unit that will ensure that the monthly profit on the sales of these units will be at least $42,000.

As per the mathematical rule, we know that:
TR - TC = total profit
Where, TR = (sell price per item) * (number of items)
And TC = (cost price per item) * (number of items)
The question asks to find the selling price per item i.e x
Therefore, by simplifying the problem, we get:
=> 600x - (600)(90) = 42,000
=> 600x - 54,000 = 42,000
=> 600x = 96,000
=> x = 160

Therefore, the minimum selling price per unit = $160

Approach Solution 3:
The problem statement declares that:
Given:

• A television manufacturer produces 600 units of a certain model each month.
• He produces it at a cost to the manufacturer of $90 per unit.
• All of the produced units are sold each month.

Find Out:

• The minimum selling price per unit that will ensure that the monthly profit on the sales of these units will be at least $42,000.

Cost price per unit = $90
Total number of units = 600
Minimum profit per month = $42000 (given that number of units made are sold by the end of the month, this is the total for 600 units)
Therefore, Profit made per unit = 42000/600 = $70 per unit
Therefore, Selling price per unit = Cost Price per unit + Profit made per unit = 90 + 70 = $160
Hence, the minimum selling price per unit = $160

“A television manufacturer produces 600 units of a certain model each”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This topic has been taken from the book “GMAT Official Guide 2021”. The candidates must evaluate the data of the GMAT Problem Solving questions and calculate properly in order to solve numerical problems. The GMAT Quant practice papers help the candidates to go through varieties of questions that will enable them to polish up their mathematical knowledge.

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