Phoenix Management helps rental property owners find renters and charges the owners one$-$half of the first month$$s rent for this service. For August $2022,$ Phoenix expects to find renters for $100$ apartments with an average first month$$s rent of $$1,000.$ Budgeted cost data per tenant application for $2022$ follow:

Professional labor: $1\mathrm{.}5$ hours at $$20\mathrm{.}00$ per hour

Credit checks: $$65\mathrm{.}00$

Phoenix expects other costs, including the lease payment for the building, secretarial help, and utilities, to be $$4,500$ per month. On average, Phoenix is successful in placing one tenant for every three applicants.

Actual rental applications in August $2022$ were $270.$ Phoenix paid $$8,400$ for $390$ hours of professional labor. Credit checks went up to $$70$ per application. Other costs in August $2022($lease$,$ secretarial help, and utilities$)$ were $$5,100.$ The average first monthly rentals for August $2022$ were $$1,100$ per apartment unit for $90$ units.

Required:

$1.($a$)$ What is the master budget variance for August $2022?($b$)$ What is the total flexible budget variance for the month? $($c$)$ What is the sales volume variance for the month?

$2.$ Determine the professional labor rate and labor efficiency variances for August $2022.$