John Fleming, chief administrator for Valley View Hospital, is concerned about the costs for tests in the hospital$$s lab. Charges for lab tests are consistently higher at Valley View than at other hospitals and have resulted in many complaints. Also, because of strict regulations on amounts reimbursed for lab tests, payments received from insurance companies and governmental units have not been high enough to cover lab costs.

Mr$.$ Fleming has asked you to evaluate costs in the hospital$$s lab for the past month. The following information is available:

Two types of tests are performed in the lab$$blood tests and smears. During the past month, $1,450$ blood tests and $4,300$ smears were performed in the lab.

Small glass plates are used in both types of tests. During the past month, the hospital purchased $21,500$ plates at a cost of $$53,105.3,300$ of these plates were unused at the end of the month; no plates were on hand at the beginning of the month.

During the past month, $3,300$ hours of labor time were recorded in the lab at a cost of $$37,785.$

The lab$$s variable overhead cost last month totaled $$29,370.$

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 $$2\mathrm{.}60$ 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{.}50$ per hour.

Overhead: Overhead cost is based on direct labor$-$hours. The average rate for variable overhead is $$8\mathrm{.}40$ 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?