Final answer:
To decide between two expansion options for keyboard production, calculate the total cost for each option and find the break-even point. Option A is cheaper until the production of 400,000 units, and beyond that, Option B becomes more cost-effective. This helps the manufacturer choose the suitable option based on forecasted demand.
Step-by-step explanation:
To determine which production expansion option is better for different ranges of demand quantity, we need to compare the total cost associated with each option against the demand. The total cost includes both the initial investment and the variable production costs. The ordinary production equipment (Option A) involves an initial cost of $8 million and a production cost of $35 per unit. In contrast, the modern production equipment (Option B) has a higher initial cost of $10 million but a lower production cost of $30 per unit.
To analyze when each option is preferable, we set up the following equations representing the total cost (TC) for each option:
- TC for Option A: TCA = $8,000,000 + $35Q
- TC for Option B: TCB = $10,000,000 + $30Q
where Q represents the quantity of keyboards produced. We find the break-even point by setting TCA equal to TCB and solving for Q:
$8,000,000 + $35Q = $10,000,000 + $30Q
This simplifies to:
$5Q = $2,000,000
Q = 400,000 units
So, for quantities up to 400,000 units, Option A is cheaper, while for quantities above 400,000 units, Option B becomes more cost-effective. This analysis helps the manufacturer ascertain which production expansion option is economically feasible based on the anticipated demand for the keyboards.