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Each month, a certain manufacturing company's total expenses are equal

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Each month, a certain manufacturing company's total expenses are equal  [#permalink]

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New post 12 Jul 2018, 01:32
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Each month, a certain manufacturing company's total expenses are equal to a fixed monthly expense plus a variable expense that is directly proportional to the number of units produced by the company during that month. If the company's total expenses for a month in which it produces 20,000 units are $570,000, and the total expenses for a month in which it produces 25,000 units are $705,000, what is the company's fixed monthly expense?

A. $27,000

B. $30,000

C. $67,500

D. $109,800

E. $135,000

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Re: Each month, a certain manufacturing company's total expenses are equal  [#permalink]

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New post 12 Jul 2018, 01:42
Bunuel wrote:
Each month, a certain manufacturing company's total expenses are equal to a fixed monthly expense plus a variable expense that is directly proportional to the number of units produced by the company during that month. If the company's total expenses for a month in which it produces 20,000 units are $570,000, and the total expenses for a month in which it produces 25,000 units are $705,000, what is the company's fixed monthly expense?

A. $27,000

B. $30,000

C. $67,500

D. $109,800

E. $135,000



We'll break our question into equations to make it easier to understand.
This is a Precise appraoch.

total expense = fixed monthly expense + variable expense --> t = f + ku (where k is a constant - we are told the variable expense in 'proportional to the amount of units)
570,000 = f + 20,000k
705,000 = f + 25,000k

Looking at our equations, it is easy to see that a difference in 5,000 units created another 705,000 - 570,000 = 135,000 dollars of revenue.
So 20,000 units must cost 135,000*4 = 540,000 dollars meaning that, from our first equation, the fixed cost is 570,000 - 540,000 = 30,000

(B) is our answer.
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Re: Each month, a certain manufacturing company's total expenses are equal  [#permalink]

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New post 12 Jul 2018, 04:27
We can observe that additional 5000 (25000-20000) items lead to $135 000 ($705000-$570000) increase.

So the total variable cost will be:
(20000/5000)*135000=540 000
(25000/5000)*135000=675 000

Fixed cost=Total cost - variable cost
570 000-540 000= 30 000
705 000- 675 000 = 30 000

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Each month, a certain manufacturing company's total expenses are equal  [#permalink]

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New post 14 Jul 2018, 13:13
Bunuel wrote:
Each month, a certain manufacturing company's total expenses are equal to a fixed monthly expense plus a variable expense that is directly proportional to the number of units produced by the company during that month. If the company's total expenses for a month in which it produces 20,000 units are $570,000, and the total expenses for a month in which it produces 25,000 units are $705,000, what is the company's fixed monthly expense?

A. $27,000

B. $30,000

C. $67,500

D. $109,800

E. $135,000

The trap is Answer A. $27 is the cost per unit.

That figure is used to calculate variable cost (variable cost total changes because the number of units produced changes)

Variable Cost = (Per unit cost) * (# of units)

Fixed Cost is a cost that does not change that is incurred with each and every production batch irrespective of number of units.

Fixed Cost = (Total Cost - Variable Cost)

(1) Total cost of "extra" units?
How many [relatively] extra units cost how much total?

Fixed cost + 25,000 units = $705,000
Fixed cost + 20,000 units = $570,000

Subtract bottom from top: 5,000 units cost $135,000

(2) Cost per unit:
\(\frac{TotalCost}{No.Of.Units}=\frac{$135,000}{5,000}=$27\) per unit

Per unit cost is $27, but $27 per unit is above and beyond some fixed cost that is the same for every production batch. We need that fixed cost.

(3) Fixed cost
Fixed cost = Total cost - (Variable Cost)

Pick one production batch. Doesn't matter which one.

Variable Cost = (# of units) * (cost per unit = $27)

Variable Cost of 20,000 units:
\(($27 * 20,000) = $540,000\)

Total Cost of 20,000 units:\($570,000\)

Fixed Cost: \(($570,000 - $540,000) = $30,000\)

Answer B
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Re: Each month, a certain manufacturing company's total expenses are equal  [#permalink]

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New post 14 Jul 2018, 19:34
Bunuel wrote:
Each month, a certain manufacturing company's total expenses are equal to a fixed monthly expense plus a variable expense that is directly proportional to the number of units produced by the company during that month. If the company's total expenses for a month in which it produces 20,000 units are $570,000, and the total expenses for a month in which it produces 25,000 units are $705,000, what is the company's fixed monthly expense?

A. $27,000

B. $30,000

C. $67,500

D. $109,800

E. $135,000


Note:

Fixed cost will not change regardless the number of units produced.

***** If amount changes , that change must be occurred because of Variable cost.

Workings :

For 20000 units total cost is 570000
for 25000 units total cost is 705000

*** For 5000 units cost is increased by 135000.
This 135000 is your variable cost for 5000 units. Note: Fixed cost remains same in all condition.

Variable cost per unit :

135000 / 5000

= 27 / unit.


We know ,

Total cost = Fc + Vc
570000 = Fc + (20000*27)..........(vc = 27 / unit for 20000 units)

570000 - 540000 = Fc

Fc = 30000.

Thus the best answer is B.
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Re: Each month, a certain manufacturing company's total expenses are equal  [#permalink]

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New post 14 Jul 2018, 20:00
Bunuel wrote:
Each month, a certain manufacturing company's total expenses are equal to a fixed monthly expense plus a variable expense that is directly proportional to the number of units produced by the company during that month. If the company's total expenses for a month in which it produces 20,000 units are $570,000, and the total expenses for a month in which it produces 25,000 units are $705,000, what is the company's fixed monthly expense?

A. $27,000

B. $30,000

C. $67,500

D. $109,800

E. $135,000



Since the expense are inclusive of a certain constant amount and variable expense, so the difference in cost will be the difference in cost of variables only..
So cost of 25000-20000=705000-570000=135000
Cost of 5000=135000, so cost of 5000*4 or 20000=135000*4=540000
If the variable cost of 20000 is 540000, the constant cost will be the remaining that is 570000-540000=30000

B
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Re: Each month, a certain manufacturing company's total expenses are equal   [#permalink] 14 Jul 2018, 20:00
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