Final answer:
To calculate the total costs for 64,000 units, the variable cost per unit is determined ($3.75) and added to the fixed costs, resulting in approximately $640,000 in total costs.
Step-by-step explanation:
The student has asked how to calculate the total costs if the volume increases to 64,000 units, given that Left Hand, Inc. has fixed costs of $400,000 and that the total costs (fixed and variable) are $550,000 when 40,000 units are produced. To find the total costs at the new production level, we must first determine the variable cost per unit at the original production level.
This is done by subtracting the fixed costs from the total costs and then dividing by the number of units produced.
Variable cost per unit = (Total costs - Fixed costs) / Number of units = ($550,000 - $400,000) / 40,000 units = $3.75 per unit
Once we know the variable cost per unit, we can estimate the total costs at the new production level by adding the fixed costs to the variable costs (calculated as variable cost per unit times the new number of units).
Total costs at new volume = Fixed costs + (Variable cost per unit * New number of units) = $400,000 + ($3.75 * 64,000 units) = $400,000 + $240,000 = $640,000
Therefore, the total costs if the volume increases to 64,000 units are approximately $640,000, which is rounded to the nearest dollar as instructed.