$\frac{1}{10(min)}\frac{2}{10(min)}{3}_{10(min)}\frac{\sqrt[\phantom{2}]{4}}{25(min)}\frac{\sqrt[5]{5}}{5(min)}$

$5$

Prob. $1(25$ points$)$

Drexel hair salon offers high$-$quality hairstyling and physical relaxation services at a reasonable price, so it has unlimited demand. The service process consists of five activities $($i$.$e$.,$ five workers$)$ conducted sequentially. Activity $1$: Welcome and offer the customer a cup of coffee or tea $(10$min$)$; Activity $2$ : Wash and condition hair $(10$ min$)$; Activity $3$: Stress release massage $(10$ min$)$; Activity $4$: Design the hairstyle and do the hair $(25$min; Activity $5$: Ring up the customer's bill $).$ Find the following for a typical $8-$hour workday from $9$:$00$ a$.$m$.$ to $5$:$00$ p$.$m$.$

$($a$)$ Which activity is the bottleneck?

Activity $4$: Design $/$ Do hairstyle

$($b$)$ What is the capacity of the hair salon per hour?

$86$ customers

$2($c$)$ What is the utilization of the employee at activity $3?$

$\frac{10}{60}=16\mathrm{.}7\%or$

$($d$)$ What is the cycle time?

$25$min

$($e$)$ What is the flow rate?

$1$ costomer $/$ hr