a company sells its product for $2.50 per unit. Variable cost per unit is 1.6 and fixed costs are 40,000 per month. The plant can produce 30,000 units/month.

it is predicted that demand will exceed 30,000, so the company can use an additional plant. This plant produces units selling for the same price, with a variable cost per unit of 1.75 and a fixed cost of 2000 per month. Can someone type out the steps in computing the break-even point please? According to the book, the answer is 50,000 units, but I got 47112. Since I probably did it wrong, would anyone mind helping me out?

thanks.

Plant 1
SP 2.5
VC 1.6
CM 0.9
FC 40,000

Plant 2
SP 2.5
VC 1.75
CM 0.75
FC 2,000

Since Plant 1 has the higher CM, you will max that plant out first, so 30,000 will be made at Plant 1.

Therefore…
Plant 1
CM 0.9 x 30,00
LESS: FC 40,000
NET LOSSS: 13,000

Plant 2
CM 0.75
Less Fixed Costs: 2,000
Net Income (needs to be 13,000 to off set plant 1 loss)
0.75x – 2,000 = 13,000
0.75x = 15,000
x = 20000

Therefore, the BE is 30,000 at Plant 1 and 20,000 at Plant 2 for a total of 50,000 units