A division of a corporation manufactures bicycle pumps. Each pump sells for $9, and the variable cost of producing each unit is 40% of the selling price. The monthly fixed costs incurred by the division are $50,000. What is the break-even point for the division?

a) break-even production 1,852 units; break-even revenue $166,662
b) break-even production 1,852 units; break- even revenue $83,331
c) break-even production 9,259 units; break- even revenue $166,662
d) break-even production 9,259 units; break- even revenue $83,331

thank you

let the number of units be x

return = 9x

cost = .4(9x) + 50000

at "break-even" point, they are equal
9x = 3.6x + 50000
5.4x = 50000
x = 9259

carry on

To find the break-even point for the division, we need to determine the number of units the division needs to sell in order to cover its fixed costs.

First, let's calculate the variable cost per unit. The variable cost is 40% of the selling price, which is $9. So, the variable cost per unit is 40% * $9 = $3.60.

The contribution margin per unit is the selling price minus the variable cost per unit. Therefore, the contribution margin per unit is $9 - $3.60 = $5.40.

To cover the fixed costs of $50,000, we need to divide the fixed costs by the contribution margin per unit: $50,000 / $5.40 = 9,259.26 units.

Since the break-even point must be a whole number of units, we round up to the nearest whole number: 9,260 units.

Now, let's calculate the break-even revenue. The break-even revenue is the break-even production (9,260 units) multiplied by the selling price ($9 per unit): 9,260 units * $9 = $83,340.

Therefore, the correct answer is d) break-even production 9,259 units; break-even revenue $83,331.

To determine the break-even point for the division, we need to calculate the number of units they need to produce and the corresponding revenue to cover both the variable and fixed costs.

The variable cost is given as 40% of the selling price. Since each pump sells for $9, the variable cost per unit is 0.40 * $9 = $3.60.

The monthly fixed costs incurred by the division are $50,000.

Let's denote the break-even production as X (number of units).

The total cost can be calculated as the sum of the variable cost and the fixed cost:
Total Cost = Variable Cost per Unit * Number of Units + Fixed Cost
Total Cost = $3.60 * X + $50,000

The break-even point occurs when the total cost equals the total revenue (which is equal to the selling price per unit multiplied by the number of units):
Total Revenue = Selling Price per Unit * Number of Units
Total Revenue = $9 * X

Setting the total cost equal to the total revenue to find the break-even point:
$3.60 * X + $50,000 = $9 * X

Solving for X:
$50,000 = $9 * X - $3.60 * X
$50,000 = $5.40 * X
X = $50,000 / $5.40
X ≈ 9,259

Therefore, the break-even production for the division is approximately 9,259 units.

To calculate the break-even revenue, we can substitute the value of X back into the total revenue equation:
Total Revenue = $9 * 9,259 = $83,331

Hence, the correct option is d) break-even production 9,259 units; break-even revenue $83,331.