SOLUTION: Can someone please help me with this problem: The monthly data are provided: Unit selling price: Standard = $100 ; Premium = $150 Variable manufacturing costs: Standard = $6

Question 174151: Can someone please help me with this problem:
The monthly data are provided:
Unit selling price: Standard = $100 ; Premium = $150
Variable manufacturing costs: Standard = $60; Premium = $90
Variable selling and administrative costs: Standard = $15 ; Premium = $10
Estimated unit sales per month: Standard = $1,000 ; Premium = $2,000
Total monthly fixed costs are expected to be $15,000. What is the break-even volume in sales dollars at the expected sales mix?
a. $25,714
b. $45,000
c. $48,000
d. $60,000
Answer by Mathtut(3670) (Show Source):
You can put this solution on YOUR website!
To compute the break-even point for a company:
Sales – Variable Costs = Contribution Margin
Contribution Margin – Fixed Costs = Net Income (which should be 0 to calculate the break-even point
:
contribution margin -15000 must equal zero
:
CM-15000=0......so CM=15000
:
we are working backward here so now
:
Sales(S)-VC=CM(15000)
lets call the number of standard units sold x
lets call the number of premium units sold y
Sales-VC(standard)+Sales-VC(premium)=15000
:
100x-75x+150y-100y=15000
:
25x+50y=15000.....eq 1
:
according to the sales mix ration of x to y is $1000 to $2000
:

:
1000y=2000x--->x=1/2y.....eq 2
:
take x's value from eq 2 and plug it into eq 1
:
25(y/2)+50y=15000
:
25y+100y=30000... multiplied all terms by 2
:
125y=30000
:
y=240
:
x=1/2(240)=120
:
so to figure out total sales
:
to break even
:
C is your answer