Hi AbeNeedsAnswers,

We're told that a company will sell each unit of a new product at a price of $2 and that the variable costs per unit in each production run are estimated to be 40% of the selling price. There are also fixed costs for each production run of $5,040. We're asked for the number of units of the new product that will need to be sold for the revenue to equal their total costs for each production run.

This question can be solved in a couple of different ways. Here's how you can take advantage of the 'spread' of the Answer choices and TEST THE ANSWERS.

To start, we know that the revenue will have to make up well OVER $5,040 (the fixed costs alone are $5,040, then we also have the variable costs). Since the selling price is just $2/unit, we're going to need far MORE than $5,040/2 = 2520 units... so we can eliminate Answers C, D and E.

Let's TEST Answer A: 4200 units
IF... there are 4200 units...
Revenue = 4200($2) = $8400
Variable Cost = 4200($0.80) = $3360
Fixed + Variable Costs = $3360 + $5040 = $8400
The revenue matches the costs, so this MUST be the answer!

Final Answer: A

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

AbeNeedsAnswers wrote:Company Q plans to make a new product next year and sell each unit of this new product at a selling price of $2. The variable costs per unit in each production run are estimated to be 40% of the selling price, and the fixed costs for each production run are estimated to be $5,040. Based on these estimated costs, how many units of the new product will Company Q need to make and sell in order for their revenue to equal their total costs for each production run?

A. 4,200
B. 3,150
C. 2,520
D. 2,100
E. 1,800

A

Let x = number of units Company Q must make to break even
So, 2x = REVENUE from selling x units

As for EXPENSES, we have:
Fixed cost = 5040
Variable cost = 40% of total selling price = 40% of 2x = (0.4)(2x) = 0.8x
So, TOTAL EXPENSES = 5040 + 0.8x

We want the revenue to equal the expenses.
So, we want: 2x = 5040 + 0.8x
Subtract 0.8x from both sides: 1.2x = 5040

At this point, we have several options to solve this equation. Here's one:
Take: 1.2x = 5040
Rewrite 1.2 as fraction to get: (6/5)x = 5040
Multiply both sides by 5 to get: 6x ≈ 25,000
ASIDE: Since the answer choices are reasonably spread apart, it should be fine to use approximation

Divide both sides by 6 to get: x ≈ 25,000/6
Since 24,000/6 = 4,000, we know that 25,000/6 = a number that's BIGGER THAN 4,000

Only one answer choice (A) is bigger than 4,000

Answer: A

Cheers,
Brent

AbeNeedsAnswers wrote:Company Q plans to make a new product next year and sell each unit of this new product at a selling price of $2. The variable costs per unit in each production run are estimated to be 40% of the selling price, and the fixed costs for each production run are estimated to be $5,040. Based on these estimated costs, how many units of the new product will Company Q need to make and sell in order for their revenue to equal their total costs for each production run?

A. 4,200
B. 3,150
C. 2,520
D. 2,100
E. 1,800

A

Let's let n = the number of units sold in order to break even. The variable cost per unit is 0.4 x 2 = 0.8; thus, the variable cost for n units is 0.8n. We know that the fixed cost is $5040 and the revenue is 2n. We can create the following equation, equating total cost to total revenue:

0.8n + 5,040 = 2n

5,040 = 1.2n

4,200 = n

Answer: A