$2.$ For a process with $3$ resource pools, the following information is provided on the number of available resources in each pool, along with the required time each resource needs to finish a task.

$2-1.$ What is the capacity of each resource pool $($please fill in the table below$)(6$ points$)$

Resource Pool i Unit Load $($minutes per order$)$ Number of Units in the Resource Pool Effective Capacity of a Resource Pool $($Orders per hr$)$

A $58$

B $55$

C $46$

$2-2.$ What is this process effective capacity $(3$ points$)$

$2-3.$ Which resource pool is a bottleneck? $(3$ points$)$

$2-4.$ If the Throughput is equal to the process effective capacity that you calculated in question $2-2,$ what is the capacity utilization rate for the resource pool that is the bottleneck? $(3$ points$)$

$2-5.$ If the duration of steps that are performed by resource pool $3$ can be reduced from $4$ minutes to $3$ minutes for the task, what will be the theoretical capacity of resource pool $3?(3$ points$)$

$2-6.$ What will be the new effective capacity of the process in this case? $(3$ points$)$

$2-7.$ If the process throughput is measured and turns out to be only $20$ orders per hour, what type of improvement solutions should be looked into, to help improving the process throughput? Name $3$ prospective solutions that have to be considered. $(5$ points$)$

Hint: Identify the type of bottleneck, and specify the diagnosis and solutions based on your identified type of bottleneck from the calculations.