$4.$ Paulson$$s Piano Service, Inc. is trying to establish the standard labor cost of tuning a typical piano. The following data have been collected from time and motion studies conducted over the past three months.

Actual time spent on tuning a piano $1\mathrm{.}25$ hours

Hourly wage rate $$50$

Payroll taxes $12\%$ of wage rate

Setup and downtime $5\%$ of actual labor time

Travel and rest periods $15\%$ of actual labor time

Fringe benefits $20\%$ of wage rate

Instructions

$($a$)$ Determine the standard direct labor hour per each piano that is tuned.

$($b$)$ Determine the standard direct labor hourly rate.

$($c$)$ Determine the standard direct labor cost per each piano that is tuned.

$($d$)$ If it took $1\mathrm{.}65$ hours to tune a piano at the standard hourly rate, what was the direct labor quantity variance?

$($e$)$ During the month of May, Paulson$$s Piano service tuned $80$ pianos. The average time spent on each piano was $1\mathrm{.}75$ hours. The average cost per hour was $$62\mathrm{.}25$ per hour. Paulson$$s had to hire some less experienced part$-$time help to handle the demand.

$(1)$ Calculate the direct labor price variance.

$(2)$ Calculate the direct labor quantity variance.

$(3)$ Calculate the total direct labor variance.

$(4)$ Explain what might have caused the variances.