# Need help for my homework, wordy math problem

Given a manufacturing line of 4 phases with:

Phase 1 (5s) -> Phase 2 (10s) -> Phase 3 (8s) -> Phase 4 (7s) -> finished

In each phase, there can only be 1 product under working ( maximum capacity of 1). A product must follow this process. Assuming there is no failure in the manufacturing line, calculate the total number of output after time T= 100s and T= n (second)

My attempt: i tried to calculate the interval after the first product is finished which is 7 second. It seems wrong to me and i dont know whether there is better approach

• Let me know if my question is ambiguous. Thanks!
– D H
Commented Oct 5, 2020 at 10:57
• it's better to mention what you tried as well. Commented Oct 5, 2020 at 10:59
• @zaira I have updated my attempt
– D H
Commented Oct 5, 2020 at 11:18
• The way I read this is that a product is manufactured by going through all four phases of production, so the time it takes to manufacture a product would be the sum of the times for each phase. Commented Oct 5, 2020 at 11:29
• @N.F.Taussig yes but different products can be worked on simultaneously in different phases
– D H
Commented Oct 5, 2020 at 11:43

Assuming you start the process with nothing in the pipeline, the first item is completed in $$30$$ seconds; and then every $$10$$ seconds thereafter, another item is completed.
$$\begin{array}{cc|c|c|c|c} &\rm{phase}&1&2&3&4\\ \rm{item}&&&\\ 1&&0-5&5-15&15-23&23-30\\ 2&&5-10&15-25&25-33&33-40\\ 3&&10-15&25-35&35-43&43-50\\ 4&&15-20&35-45&45-53&53-60\\ \vdots&&\vdots&\vdots&\vdots&\vdots& \end{array}$$