Answer:
To calculate the variance of Total Payroll next week when hourly wages increase by 10% and all other costs stay constant, you need to understand how Total Payroll is calculated and then determine how the variance in hourly wages affects it.
Total Payroll is typically calculated by multiplying the number of hours worked by the hourly wage. In a simplified formula:
Total Payroll = Hours Worked * Hourly Wage
Let's assume that the current week's Total Payroll is $X.
Next week, hourly wages are going to increase by 10%. So, the new hourly wage will be 110% of the current hourly wage.
If the current hourly wage is WW, then the new hourly wage will be 1.10W1.10W.
Now, let's calculate Total Payroll next week, denoted as YY:
Y=Hours Worked×1.10WY=Hours Worked×1.10W
To calculate the variance in Total Payroll between next week and the current week, you can use the following formula:
Variance = (Y−X)2(Y−X)2
Plug in the values:
Variance = (Hours Worked×1.10W−Hours Worked×W)2(Hours Worked×1.10W−Hours Worked×W)2
Now, factor out Hours Worked2Hours Worked2 and W2W2:
Variance = (Hours Worked2×(1.102−1)2×W2)(Hours Worked2×(1.102−1)2×W2)
Variance = Hours Worked2×(1.102−1)2×W2Hours Worked2×(1.102−1)2×W2
Variance = Hours Worked2×0.21×W2Hours Worked2×0.21×W2
So, the variance of Total Payroll next week will be 0.210.21 times the square of the product of the number of hours worked and the current hourly wage. This variance is due to the 10% increase in hourly wages.