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Each month, a certain manufacturing company's total expenses
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18 Nov 2018, 03:14
18 Nov 2018, 03:14
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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
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
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21 Dec 2021, 04:39
21 Dec 2021, 04:39
1
Here we can call the Fixed Expense x and the Variable Expense y.
Therefore, we see that x + 20,000*y = 570,000, while x + 25,000*y = 705,000.
This simply gives us two equations and two unknowns so we can stack them up to eliminate the x-value:
x + 20,000*y = 570,000
x + 25,000*y = 705,000
----------------------
5000*y = 135,000
y = 135,000 / 5000 = 27
Now just plug this back into either equation to get the answer:
x + 27*20,000 = x + 540,000 = 570,000
==> x = 570,000 - 540,000 = 30,000.
Answer B.
Therefore, we see that x + 20,000*y = 570,000, while x + 25,000*y = 705,000.
This simply gives us two equations and two unknowns so we can stack them up to eliminate the x-value:
x + 20,000*y = 570,000
x + 25,000*y = 705,000
----------------------
5000*y = 135,000
y = 135,000 / 5000 = 27
Now just plug this back into either equation to get the answer:
x + 27*20,000 = x + 540,000 = 570,000
==> x = 570,000 - 540,000 = 30,000.
Answer B.
General Discussion
Re: Each month, a certain manufacturing company's total expenses
[#permalink]
25 Nov 2018, 12:12
25 Nov 2018, 12:12
4
Explanation:
Let F = fixed monthly expense
V = Variable expense.
As per 1st equation,
F + 20,000V = 570,000 ------------------(1)
and
F + 25,000V = 705,000 -------------------(2)
Solving equation (1) and (2)
V = 27.
Putting the value of V in equation 1,
F = 30,000, i.e Option B
Let F = fixed monthly expense
V = Variable expense.
As per 1st equation,
F + 20,000V = 570,000 ------------------(1)
and
F + 25,000V = 705,000 -------------------(2)
Solving equation (1) and (2)
V = 27.
Putting the value of V in equation 1,
F = 30,000, i.e Option B
