Question $4[12]$

A company makes $200$ batches of a certain product, per month. The batch size is $10$ units. The entire manufacturing process involves $5$ machines. Set$-$up time is $1$ hour, operation time $\backslash (=12\backslash$mathrm$\{$~min$\}\backslash )$ per unit. Non$-$operation time $\backslash (=3\backslash )$ hours.

The plant operates $8$ hours per day, $25$ days per month. If waste is negligible, determine:

$4\mathrm{.}1$ The manufacturing lead$-$time for a batch

$4\mathrm{.}2$ The annual plant capacity

$4\mathrm{.}3$ The plant utilization

Question $5[10]$

A batch production process has a batch size of $50$ units and a setup time of $1$ hour $45$ min $.$ Part handling time is $15$ seconds. Processing time is $2\mathrm{.}5$ min $.$ A new tool must be used every $5$ parts. Tool changes take $2$ min to complete.

$5\mathrm{.}1$ Calculate the average cycle time

$5\mathrm{.}2$ Calculate the batch time

$5\mathrm{.}3$ Calculate the production rate

Question $6[7]$

A machine shop has $10$ machines. The setup time averages $4$ hours. Batch size is $6.$ The average operation time $\backslash (=1\mathrm{.}0\backslash )$ minute. The shop operates $8-$hours per day, $25$ days per month. Scrap losses are negligible.

$6\mathrm{.}1$ Calculate the monthly production capacity.

Question $7[9]$

An NC machine has a leadscrew with pitch $\backslash (=5\mathrm{.}0\backslash$mathrm$\{$~mm$\}\backslash )$ and is connected to a servomotor with a gear ratio of $4$:$1(4$ turns of the motor for each turn of the lead screw$).$ An optical encoder is connected directly to the lead screw and generates $120$ pulses $\backslash (/\backslash$mathrm$\{$rev$\}\backslash )$ of the lead screw. The feed rate is $\backslash (150\backslash$mathrm$\{$~mm$\}/\backslash$mathrm$\{$min$\}\backslash ).$ Determine:

$7\mathrm{.}1$ The pulse count received by the control system to verify that the table has moved exactly $100$ mm

$7\mathrm{.}2$ The pulse rate

$7\mathrm{.}3$ Motor speed