What would be the budgeted production cost of 16 000 units?

• Direct labour:
  • Cost for 10,000 units: $6,800
  • Cost for 20,000 units: $13,600
  • Since 13,600 = 2 \times \6,800$, direct labour is a variable cost.
  • Variable cost per unit for direct labour: \frac{\6,800}{10,000 units} = $0.68 \text{ per unit}$.
• Direct material:
  • Cost for 10,000 units: $34,000
  • Cost for 20,000 units: $68,000
  • Since 68,000 = 2 \times \34,000$, direct material is a variable cost.
  • Variable cost per unit for direct material: \frac{\34,000}{10,000 units} = $3.40 \text{ per unit}$.
• Production overheads:
  • Cost for 10,000 units: $32,000
  • Cost for 20,000 units: $40,000
  • Since the cost changes but not proportionally with output, production overheads are a mixed cost (partially fixed, partially variable).

Let $V$ be the variable cost per unit and $F$ be the fixed cost.
Using the high-low method:
Variable cost per unit for overheads:

$V = \frac{\$40,000 - \$32,000}{20,000 \text{ units} - 10,000 \text{ units}}$ $V = \frac{\$8,000}{10,000 \text{ units}} = \$0.80 \text{ per unit}$ Fixed cost for overheads:
Using the cost at 10,000 units:

$F = \$32,000 - (\$0.80 \text{ per unit} \times 10,000 \text{ units})$ $F = \$32,000 - \$8,000 = \$24,000$ Alternatively, using the cost at 20,000 units: $F = \$40,000 - (\$0.80 \text{ per unit} \times 20,000 \text{ units})$ $F = \$40,000 - \$16,000 = \$24,000$ The fixed production overheads are $24,000.

Total variable cost per unit = Variable direct labour per unit + Variable direct material per unit + Variable production overheads per unit $\text{Total variable cost per unit} = \$0.68 + \$3.40 + \$0.80 = \$4.88 \text{ per unit}$

Total cost = (Total variable cost per unit $\times$ Number of units) + Total fixed cost $\text{Total cost} = (\$4.88 \text{ per unit} \times 16,000 \text{ units}) + \$24,000$ $\text{Total cost} = \$78,080 + \$24,000$ $\text{Total cost} = \$102,080$

The calculated total cost is $102,080, which matches option B.

The budgeted production cost of 16,000 units is \boxed{\text{B } \102,080}$.