Question

NanoTech is ready to begin production of its exciting new technology. The company is evaluating three methods of production: (A) a small production facility with older equipment, (B) a larger production facility that is more automated, and (C) subcontracting to an electronics manufacturer in Singapore. Process A has a fixed cost of $200,000 and a variable cost of $40 per unit. Process B has a fixed cost of $600,000 and a variable cost of $20 per unit. Process C has no fixed cost since the item is purchased. It's variable cost is the purchase price of $60 per unit. For what levels of demand would each process be desirable

Answer 1

To choose the most cost-effective production method, perform a break-even analysis between all methods. Method A is desirable for up to 10,000 units, Method B is better for demands between 10,000 to 15,000 units, and Method C is suitable for demands of 15,000 units or more.

Step-by-step explanation:

To determine which production method is most cost-effective at different levels of demand, it is necessary to compare the total costs for each method. The total cost for each method includes both fixed and variable costs. The choice of the lowest-cost production technology can change with variations in the cost structure of labor (wages) and capital (machines).

Let's calculate the break-even points between production methods A and B, as well as between B and C:

• Method A has a fixed cost of $200,000 and a variable cost of $40 per unit.
• Method B has a fixed cost of $600,000 and a variable cost of $20 per unit.
• Method C has no fixed cost and a variable cost of $60 per unit.

Break-Even Analysis

To find the break-even point between Method A and Method B:

$200,000 + $40x = $600,000 + $20x

$200,000 = $20x

x = 10,000 units

So, for demands up to 10,000 units, Method A is more cost-effective than Method B.

To find the break-even point between Method B and Method C:

$600,000 + $20x = $60x

$600,000 = $40x

x = 15,000 units

Thereby, for demands above 10,000 but below 15,000 units, Method B is more cost-effective than both Method A and Method C. For demands of 15,000 units or more, Method C becomes the low-cost form of production.

Answer 2

Process A= from 10,001 to 19,999

Process B= 20,001 to infinity

Process C= from 0 to 9,999

Step-by-step explanation:

Giving the following information:

Process A has a fixed cost of $200,000 and a variable cost of $40 per unit.

Process B has a fixed cost of $600,000 and a variable cost of $20 per unit.

Process C has no fixed cost since the item is purchased. It's variable cost is the purchase price of $60 per unit.

The general rule is that the lower the fixed costs, the fewer units are required to cover for costs. To determine the number of units for each process, we will compare process C to A, and then A to B.

Process C and A:

Process A= 200,000 + 40x

Process C= 60x

x= number of units

200,000 + 40x= 60x

200,000= 20x

10,000 = number of units

The indifference point is 10,000 units. From 0 to 9,999; process C is more convenient.

Process A and B:

Process A= 200,000 + 40x

Process B= 600,000 + 20x

200,000 + 40x = 600,000 + 20x

20x= 400,000

x= 20,000

The indifference point is 20,000 units. From 10,001 to 19,999; process A is more convenient.