Question
A process needs to be completed n times if n units are to be produced. Only different processes can take place simultaneously. What is the minimum time (In hours) required to get two units of the final product? (Given: The final product can only be completed if both the processes W and U are over.)
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Answer:
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As 2 units of the final product are required, every process has to be completed twice.
Processes P and R are independent processes. Process P will run for 6 hours for the first time and immediately for next 6 hours for the second time. Process R will run for 4 hours for the first time and immediately for next 4 hours for the second time.
Process Q and Y start as soon as both P and R get over. i.e., process Q starts immediately after 6 hours and run for 7 hours for one unit and again for next 7 hours for the second unit. Similarly, process Y starts immediately after 6 hours and run for 14 hours for one unit and again for next 14 hours for the second unit. So, process Y will get over at the end of 20 hours for the first time and 34 hours for the second time.
Thus, at the end of first 13 hours, process Q gets over for the first time and at the end of 20 hours it gets over for the second time. Process Y will get over at the end of 20 hours for the first time and 34 hours for the second time.
So process S can start immediately after 13 hours for the first time and after 20 hours for the second time. S runs for 2 hours and finishes at the end of 15 hours and 22 hours respectively.
Now, processes U and W start immediately after 20 and 22 hours respectively and get over at the end of 30 and 31 hours respectively for the first time.
For the second time, processes U and W start immediately after 34 and 31 hours respectively and get over at the end of 44 and 40 hours respectively.
Thus, at the end of 44 hours, 2 units of the final product will be achieved.
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As 2 units of the final product are required, every process has to be completed twice.
Processes P and R are independent processes. Process P will run for 6 hours for the first time and immediately for next 6 hours for the second time. Process R will run for 4 hours for the first time and immediately for next 4 hours for the second time.
Process Q and Y start as soon as both P and R get over. i.e., process Q starts immediately after 6 hours and run for 7 hours for one unit and again for next 7 hours for the second unit. Similarly, process Y starts immediately after 6 hours and run for 14 hours for one unit and again for next 14 hours for the second unit. So, process Y will get over at the end of 20 hours for the first time and 34 hours for the second time.
Thus, at the end of first 13 hours, process Q gets over for the first time and at the end of 20 hours it gets over for the second time. Process Y will get over at the end of 20 hours for the first time and 34 hours for the second time.
So process S can start immediately after 13 hours for the first time and after 20 hours for the second time. S runs for 2 hours and finishes at the end of 15 hours and 22 hours respectively.
Now, processes U and W start immediately after 20 and 22 hours respectively and get over at the end of 30 and 31 hours respectively for the first time.
For the second time, processes U and W start immediately after 34 and 31 hours respectively and get over at the end of 44 and 40 hours respectively.
Thus, at the end of 44 hours, 2 units of the final product will be achieved.
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