Question

Big John's Manufacturing currently produces its lead product on a machine that has a variable cost of $0.32 per unit and fixed costs of $75,000. Big John is considering purchasing a new machine that would drop the variable cost to $0.28 per unit but has fixed costs of $150,000. What is the cross-over point between the two machines?

a. 100,000 units
b. 125,000 units
c. 150,000 units
d. 175,000 units

Answer 1

The correct crossover point between the two machines is 1,875,000 units (not among the provided options).

The correct option is not given.

Step-by-step explanation:

The crossover point is the point at which the total costs for both machines are equal.

The total cost for the existing machine is a combination of variable and fixed costs, and the same goes for the new machine.

Let Q be the number of units produced.

For the existing machine:

Total Cost = Fixed Cost + (Variable Cost per Unit x Q)

Total Cost = $75,000 + $0.32 x Q

For the new machine:

Total Cost = Fixed Cost + (Variable Cost per Unit x Q)

Total Cost = $150,000 + ($0.28 x Q)

At the crossover point, these two total costs are equal:

$75,000 + $0.32 x Q = $150,000 + $0.28 x Q

Now, solve for Q :

$0.32 x Q - $0.28 x Q = $150,000 - $75,000

$0.04 x Q = $75,000

Q = $75,000 / $0.04

Q = 1,875,000

So, the crossover point is 1,875,000 units.

None of the provided options (a. 100,000 units, b. 125,000 units, c. 150,000 units, d. 175,000 units) match the calculated crossover point. Please double-check the provided options or the problem statement.

The correct option is not given.