Final answer:
To compute the total budgeted costs at 73,700 direct labor hours, we need to find the equation of the total budgeted cost line. We can do this by calculating the slope of the line using two given points and then using the slope-intercept form of a linear equation to find the equation of the line. After substituting the value of 73,700 direct labor hours into the equation, we find that the total budgeted costs at 73,700 direct labor hours are $447,903.8.
Step-by-step explanation:
To compute the total budgeted costs at 73,700 direct labor hours, we need to find the equation of the total budgeted cost line. We know that the fixed-cost line and the total budgeted cost line intersect the vertical axis at $94,400. We also know that the total budgeted cost line is $380,960 at an activity level of 59,700 direct labor hours.
Using these two points, we can calculate the slope of the total budgeted cost line:
Slope = (Total budgeted cost at 59,700 hours - Total budgeted cost at 0 hours) / (59,700 hours - 0 hours)
Slope = ($380,960 - $94,400) / (59,700 - 0)
Slope = $286,560 / 59,700
Slope = $4.794 per direct labor hour
Now, we can use the slope-intercept form of a linear equation to find the equation of the total budgeted cost line:
Total budgeted cost = (slope) * (direct labor hours) + (y-intercept)
The y-intercept is the total budgeted cost at 0 hours, which is $94,400.
Total budgeted cost = $4.794 * 73,700 + $94,400
Total budgeted cost = $353,503.8 + $94,400
Total budgeted cost = $447,903.8