Question

Worthington Machining must decide whether to purchase Process A with specialized metal folding equipment needing two employees to operate it or Process B with general purpose folding equipment requiring five employees. Process A requires a fixed cost of $1,430,000 and a variable cost of $14.32 per metal panel. Process B requires a fixed cost of $820,000 and a variable cost of $20.05. Process A is more automated than Process B. What is the break-even quantity between these two processes

Answer 1

The break-even quantity between Process A and Process B, given their fixed and variable costs, is found by equating their total costs and solving for the quantity. In this case, it is 106,456 metal panels.

Step-by-step explanation:

The student is asking for a break-even analysis between two different manufacturing processes, A and B, with different fixed and variable costs. To find the break-even quantity, we compare the total costs of the two processes and solve for the quantity where they are equal.

Let the break-even quantity be represented by 'Q'. The total cost of Process A for 'Q' panels is 1,430,000 + 14.32Q, and the total cost of Process B for 'Q' panels is 820,000 + 20.05Q.

To determine the break-even point, we set these two expressions equal to each other:
1,430,000 + 14.32Q = 820,000 + 20.05Q.

Solving for 'Q' involves the following steps:
1. Subtract 14.32Q from both sides:
1,430,000 = 820,000 + 5.73Q
2. Subtract 820,000 from both sides:
610,000 = 5.73Q
3. Divide both sides by 5.73 to find 'Q':
Q = 106,456 (rounded to the nearest whole number).

The break-even quantity is 106,456 metal panels.

Answer 2

The indifference point is 106,457 units.

Step-by-step explanation:

Giving the following information:

Process A:

Fixed cost= $1,430,000

Variable cost= $14.32 per metal panel.

Process B:

Fixed cost= $820,000

Variable cost= $20.05 per metal panel.

To calculate the indifference point between two processes, first, we need to formulate the total cost equation for each process:

Process A:

Total cost= 1,430,000 + 14.32*x

Process B:

Total cost= 820,000 + 20.05*x

x= number of units

Now, we need to equal both formulas and isolate x:

1,430,000 + 14.32x = 820,000 + 20.05x

610,000 = 5.73x

x= 106,457

The indifference point is 106,457 units.