A. This is the total cost for 200 units. However, the problem asks for the total cost for the last 150 units
B. This is the total variable cost for 200 units. However, it is not the total cost, or is it the cost for the last 150 units.
C. We need to include the first 50 units manufactured in this analysis, since they contributed to the learning curve. So we will analyze the cost for the first 200 units and then subtract from that the cost for the first 50 units in order to calculate the cost for units numbered 51 through 200, which are the units in the second order of 150.
The first doubling takes place at unit no. 100. The second doubling takes place at unit no. 200. Therefore, the time required for the total 200 units was 2,560 hours, calculated as follows: 1,000 hours × (.8 × 2) × (.8 × 2) = 2,560 hours for 200 units.
2,560 hours for 200 units minus the 1,000 hours required for the first 50 units = 1,560 hours required for the last 150 units.
The next step is to calculate the total cost for the whole 200 units and then subtract from that the cost for the first 50 units, which is given in the problem as $15,400.
Using the costs for 50 units provided in the problem, we can calculate the variable costs for 200 units as follows: Direct Materials cost per unit is $1,500 ÷ 50 units, or $30 per unit. Therefore, for 200 units, the total direct materials cost would be 30 × $200, or $6,000. Direct labor is $8.50 per hour for a total of 2,560 hours, or $21,760 for 200 units. Variable overhead is applied on the basis of direct labor hours at the rate of $4 per direct labor hour; so for 2,560 DL hours, variable overhead would be $10,240.
Thus, the total variable cost for 200 units is $6,000 + $21,760 + $10,240, for a total of $38,000. Fixed overhead is applied at the rate of 10% of total variable cost, so fixed overhead applied is 10% of $38,000, or $3,800.
The total cost for 200 units is thus $38,000 + $3,800, or $41,800.
Subtracting the cost for the first 50 units from the total cost for the first 200 units, we get $41,800 - $15,400, or $26,400 as the cost for units 51 through 200.
D. This is the total cost of the labor and variable overhead for 200 units. However, it is not the total cost, nor is it the cost for the last 150 units.
