Company Q plans to make a new product next year and sell each unit

BTGModeratorVI wrote: ↑

Sat Aug 08, 2020 7:04 am

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

Answer: A
Source: Official guide

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

BTGModeratorVI wrote: ↑

Sat Aug 08, 2020 7:04 am

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

Answer: A
Source: Official guide

Solution:

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