Valley View Hospital has never used standard costs. By searching industry literature, however, you have determined the following nationwide averages for hospital labs:

Plates: Three plates are required per lab test. These plates cost $$3\mathrm{.}50$ each and are disposed of after the test is completed.Labor: Each blood test should require $0\mathrm{.}8$ hours to complete, and each smear should require $0\mathrm{.}40$ hours to complete. The average cost of this lab time is $$12\mathrm{.}00$ per hour.

Overhead: Overhead cost is based on direct labor$-$hours. The average rate for variable overhead is $$7\mathrm{.}90$ per hour.

Required:

$1.$ Compute a materials price variance for the plates purchased last month and a materials quantity variance for the plates used last month.

$2.$ For labor cost in the lab:

a$.$ Compute a labor rate variance and a labor efficiency variance.

b$.$ In most hospitals, one$-$half of the workers in the lab are senior technicians and one$-$half are assistants. In an effort to reduce costs, Valley View Hospital employs only one$-$fourth senior technicians and three$-$fourths assistants. Would you recommend that this policy be continued?

$3-$a$.$ Compute the variable overhead rate and efficiency variances.

$3-$b$.$ Is there any relation between the variable overhead efficiency variance and the labor efficiency variance?