Problem $1\mathrm{.}3$: A work group of $20$ workers in a certain month produced $8600$ units of output

working $8h\frac{r}{?}$ day for $21$ days. $($a$)$ What is the labor productivity ratio for this month? $($b$)$ In the next

month, the same worker group produced $8000$ units but there were $22$ workdays in the month and

the size of the work group was reduced to $14$ workers. What is the labor productivity ratio for this

second month? $($c$)$ What is the productivity index using the first month as a base?

Problem $1\mathrm{.}4$: There are $20$ forging presses in the forge shop of a small company. The shop

produces batches of forgings requiring a setup time of $3\mathrm{.}0$ hours for each production batch.

Average standard time for each part in a batch is $45$ seconds, and there are an average of $600$ parts

in a batch. The plant workforce consists of two workers per press, two foremen, plus three clerical

support staff. $($a$)$ Determine how many forged parts can be produced in $1$ month, if there are $8$

hours worked per day and an average of $21$ days per month at one shift per day. $($b$)$ What is the

labor productivity ratio of the forge shop, expressed as parts per worker$-$hour?

Problem $2\mathrm{.}1$: If the normal time is $1\mathrm{.}30$ min for a repetitive task that produces one work unit per

cycle, and the company uses a PFD allowance factor of $12\%,$ determine $($a$)$ the standard time for

the task and $($b$)$ how many work units are produced in an $8-$hour shift at standard performance.

Problem $2\mathrm{.}6$: A worker performs a repetitive assembly task at a workbench to assemble products.

Each product consists of $25$ components. Various hand tools are used in the task. The standard

time for the work cycle is $7\mathrm{.}45$ min $,$ based on using a PFD allowance factor of $15\%.$ If the worker

completes $75$ product units during an $8-$hour shift, determine $($a$)$ the number of standard hours

accomplished and $($b$)$ worker efficiency. $($c$)$ If the worker took only one rest break, lasting $13$ min $,$

and experienced no other interruptions during the $8$ hours of shift time, determine her worker

performance.