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Company Q plans to make a new product next year and sell each unit of [#permalink]

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17 Jun 2017, 09:39

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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?

Re: Company Q plans to make a new product next year and sell each unit of [#permalink]

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17 Jun 2017, 09:48

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AbdurRakib 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

Let the total number of units be x.

Selling price of total x units = $2x

Total Cost price = 5040 + 40% of selling price $2x

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

The variable costs per unit = 0.4*2 = $0.8. So, we are left with $1.2.

To break even with $5,040 of fixed costs, $5,040/1.2 = $5,040*5/6 = 4,200 units should be made.

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

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

Re: Company Q plans to make a new product next year and sell each unit of [#permalink]

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22 Aug 2017, 07:58

AbdurRakib 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

Total Cost = Fixed Cost + Variable Cost

Or, Total Cost = Fixed Cost + (Cost Price per unit x No of Units Produced)

Here, Variable Cost is 0.8

So, Total Cost = 5040 + 0.80*n (Where n = Number of Units produced)

Total Revenue = No of Units Sold x Selling Price of each unit

So, Total Revenue = 2n

Quote:

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?

\(5040 + 0.80n = 2n\)

Or, \(n = \frac{5040}{1.20}\)

Or, \(n = 4200\)

Hence, the correct answer must be (A) 4200 _________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

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

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
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