$3$

Problem $1(20$ pts$)$:

A manufacturing company has received an order to machine $1000$ parts. For quality assurance, one sample for every $20$ samples has to be tested for tensile strength. The starting work part costs $12\mathrm{.}50$ SR$,$ each. Part handling time for each cycle $=5\mathrm{.}3$min, and machining time per part $=7\mathrm{.}25$min. It takes $150$ min to set up the machine for the whole production. Equipment cost rate $=63\mathrm{.}00S\frac{R}{h}r,$ and labor cost rate $=35\mathrm{.}00S\frac{R}{h}r.$ The overhead cost is $37\%$ of the labor and equipment cost rates. The cutting tool in the operation costs $=152\mathrm{.}00SR,$ and it must be changed every $26$ parts. Tool change time $=6\mathrm{.}45$min. Availability of the machine tool $=94\mathrm{.}0\%,$ in addition, the defect rate is $3\%.$ Determine:

a$)$ required time $($hours$)$ to complete the batch;

b$)$ production rate of good parts;

c$)$ total cost of the batch;