Please answer this with step by step solution: a$)$ Calculate the takt time $($in seconds$).$ b$)$ Calculate the production lead time for the process. DATA SET TastyJuice Co$.$ produces multiple types of juices for their customer DistribJuice, which is a juice distribution company. This case concerns one type of juice: A mixed fruit juice called DeliciousDrink. CUSTOMER REQUIREMENTS: $25,000$ bottles of juice per month Customer plant operates on two shifts Bottles are sent to DistribJuice in crates that hold $50$ bottles$/$crate$.$ Multiple cranes are sent to the customers. Bi $-$ weekly shipment to DistribJuice by truck $($once every two weeks$)$ WORK TIME: $24$ days in a month Two shift operation in all production departments Eight $(8)$ hours every shift. Three $10$ minute breaks during each shift Lunch time of $30$ min Manual processes stop during breaks. PRODUCTION PROCESSES: $-$ Tasty Juice's process for this product family involves $5$ steps: preparing ingredients for mixing, mixing, making juice, bottling, and sealing. After sealing the bottles are shipped to DistribJuice on a bi$-$ weekly basis. The ingredients are supplied by JuiceSupply Co$.-$ Deliveries from JuiceSupply are made to Tasty Juice on Wednesdays. TASTYJUICE PRODUCTION CONTROL DEPARTMENT: TastyJuice receives DistribJuice's $180/90/30-$ day forecasts and enters them to MRP Tasty Juice issues $4$ week forecasts to JuiceSupply $-$weekly build schedules to Preparation, Mixing, Making Juice, Bottling and Sealing

processes $-$ TastyJuice issues bi $-$ weekly shipping schedule to Shipping Department

PROCESS INFORMATION: All processes occur in the following order and each item goes through all processes. $1)$ PREPARATION FOR MIXING Manual process with one operator

$-$ Cycle Time: $40$ seconds Changeover time: $1$ hour Uptime: $100\%$ Observed

Inventory: $7$ days of materials before preparation station. Observed inventory: $1000$ units $($Inventory after Prep for Mixing but before Mixing. Observed inventory is given for the inventory that immediate follows the workstation $($and before the next workstation$)$ unless otherwise noted $2)$ MIXING Automated process done with $1000-$ ton mixer. Cycle lime:

$10$ seconds Changeover time: $30$ minutes Uptime: $100\%$ Observed Inventory: $2000$

units$13)$ JUICE MAKER Automated process done with $1000-$ ton juice maker. $-$ Cycle

lime: $20$ seconds Changeover time: $20$ minutes Uptime: $100\%$ Observed Inventory:

$-$

$3200$ units $4)$ BOTTLING Automated process done with bottling machine $-$ Cycle lime:

$60$ seconds Changeover time: $60$ minutes Uptime: $100\%$ Observed Inventory: $800$

units $5)$ SEALING Manual process with one operator Cycle Time: $15$ seconds

Changeover time: $10$ minutes Uptime: $100\%$ Observed Inventory: $2500$ units $6)$

SHIPPING DEPARTMENT Removes parts from finished goods warehouse and stages them for truck shipment to customer. $1$ This machine holds mixed liquid, but rather than reporting volume of liquid, we have info on how many units of inventory that