Answer:
a. break even number in units = $250,000 / $10.0908 = 24,775.04
red units = 24,775.04 x 5/11 = 11,261.38 ≈ 11,262 units
total sales = 11,262 x $20 = $225,240
white units = 24,775.04 x 4/11 = 9,009.11 ≈ 9,010 units
total sales = 9,010 x $35 = $315,350
blue units = 24,775.04 x 2/11 = 4,504.55 ≈ 4,505 units
total sales = 4,505 x $65 = $292,825
total sales = $833,415
b. new break even number in units = $300,000 / $19.4545 = 15,420.60
red units = 15,420.60 x 5/11 = 7,009.36 ≈ 7,010 units
total sales = 7,010 x $20 = $140,200
white units = 15,420.60 x 4/11 = 5,607.49 ≈ 5,608 units
total sales = 5,608 x $35 = $196,280
blue units = 15,420.60 x 2/11 = 2,803.75 ≈ 2,804 units
total sales = 2,804 x $65 = $182,260
total sales = $518,740
c. Management should start using the new material as soon as possible since it doesn't only decrease the break even point, if sales level remain the same, it will increase operating profits.
Explanation:
red's contribution margin = $8
white's contribution margin = $13
blue's contribution margin = $12
sales mix = 5:4:2
weighted contribution margin = ($8 x 5/11) + ($13 x 4/11) + ($12 x 2/11) = $3.6363 + $4.2727 + $2.1818 = $10.0908
new contribution margin:
red's contribution margin = $14
white's contribution margin = $25
blue's contribution margin = $22
sales mix = 5:4:2
weighted contribution margin = ($14 x 5/11) + ($25 x 4/11) + ($22 x 2/11) = $6.3636 + $9.0909 + $4 = $19.4545
