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

Question

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

A. $27,000

B. $30,000

C. $67,500

D. $109,800

E. $135,000

DavidTutorexamPAL · Answer

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.

LevanKhukhunashvili · Answer

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

In My Opinion
Ans:  B

generis · Answer

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   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

KSBGC · Answer

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.

chetan2u · Answer

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

ScottTargetTestPrep · Answer

Solution:

If we let x = the number of units produced, m = the unit cost and b = the fixed expense, then y, the total monthly expenses, can be determined by the equation y = mx + b. We can create the equations:

570,000 = m(20,000) + b

and

705,000 = m(25,000) + b

Subtracting the first equation from the second, we have:

135,000 = 5,000m

27 = m

Substituting 27 for m in the first equation, we have: 
 
570,000 = (27)(20,000) + b

570,000 = 540,000 + b

30,000 = b

Answer: B

daniformic · Answer

570-30 (i suggest trying first with answer B)=540/20=27
705-30=675/25=27 BINGO!

Answer B

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

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