Final answer:
To find the total cost of producing 10,000 units, we can use the high-low method. By calculating the variable and fixed costs for each cost type, we can determine the total cost. In this case, the total cost would be -$5,968.
Step-by-step explanation:
To find the total cost of producing 10,000 units, we can use the high-low method. The high level of activity is 7,500 units, and the low level is 5,000 units. We can calculate the variable cost per unit for each cost type by finding the difference in cost and dividing it by the difference in activity level. For Type A, the variable cost is ($7 - $7) / (7,500 units - 5,000 units) = $0 / 2,500 units = $0 per unit. For Type B, the variable cost is ($12 - $18) / (7,500 units - 5,000 units) = -$6 / 2,500 units = -$2.40 per unit. For Type C, the variable cost is ($6 - $7) / (7,500 units - 5,000 units) = -$1 / 2,500 units = -$0.40 per unit.
Next, we can calculate the fixed cost for each cost type by subtracting the variable cost per unit from the total cost at the high level of activity. For Type A, the fixed cost is $7 - ($0 per unit * 7,500 units) = $7. For Type B, the fixed cost is $18 - (-$2.40 per unit * 7,500 units) = $18 - (-$18,000) = $18 + $18,000 = $18,018. For Type C, the fixed cost is $7 - (-$0.40 per unit * 7,500 units) = $7 - (-$3,000) = $7 + $3,000 = $3,007.
Finally, we can calculate the total cost by multiplying the variable cost per unit by the number of units and adding the fixed cost for each cost type. For Type A, the total cost is ($0 per unit * 10,000 units) + $7 = $0 + $7 = $7. For Type B, the total cost is (-$2.40 per unit * 10,000 units) + $18,018 = -$24,000 + $18,018 = -$5,982. For Type C, the total cost is (-$0.40 per unit * 10,000 units) + $3,007 = -$4,000 + $3,007 = -$993.
When we add up the total costs for each cost type, the total cost of producing 10,000 units is $7 + (-$5,982) + (-$993) = $7 - $5,982 - $993 = -$5,968.