You must indicate units for your final responses $($e$.$g$.,$ vases per minute or vases per hour$)$ and show your calculations or provide reasoning as applicable to indicate how you arrived at your responses, otherwise you will not get credit for them.

$1.$ A production process for flower vases consists of three tasks to be completed in sequence: first, Shape $($by a specialized machine$),$ second, Bake $($in a single oven$),$ and third, Paint $($by a worker$).$ The times taken for one vase at each step are $5$ minutes for Shape, $8$ minutes for Bake, and $6$ minutes for Paint. There are $8$ working hours in each day.

Assume that there is one resource at each step. Indicate, showing your calculations, what is the daily capacity of each activity $($i$.$e$.,$ shape, bake, and paint$)$ in units$/$vases per day? $(30$ points$)$

$2.$ Indicate which is the bottleneck task, and why? $(10$ points$)$

$3.$ If the demand for flower vases is $50$ units per day, what will be the flow rate $($per day$)$ of the original process? $(10$ points$)$

$4.$ Assume no waiting between steps, what is the throughput time of the process $($in minutes$).(10$ points$)$

$5.$ If a second oven, identical to the first one, is added to the Bake task, what is the new throughput time of the whole process $($in minutes$)?(10$ points$)$

$6.$ If a second oven, identical to the first one, is added to the Bake task, what is the new daily capacity of the whole process? $(10$ points$)$

$7.$ A restaurant chain with several locations in Champaign County wants to assess the freshness of the meat used in their hamburgers and has requested your expertise for the task. The

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average inventory of raw meat in their centralized production facility is $1,200$ pounds and the restaurant chain sells, on average, burgers totaling $300$ pounds of meat content every day. Please help by calculating how many days the hamburger meat spends in the process. Among the three elements in Little's Law, what are we trying to figure out here? $(5$ pts$)$

$8.$ How many days the hamburger meat spends in the process $($in numerical numbers$)?(5$ pts$)$

$9.$ If the Champaign restaurant chain were to reduce the amount of average inventory that they maintain in their centralized production facility from the current amount of $1,200$ pounds to $900$ pounds and everything else stays the same, what impact would it have on the freshness of the meat in terms of how many days on average the meat spends in the process? Please show your calculations$/$reasoning$.(10$ points$)$