Minimize finish time of two sequential tasks

Give a direct mathematical answer to this tiny scheduling problem. There is one unit-capacity resource R. Task P takes 4 time units on R, is released at time 0 and has no predecessor. Task Q takes 2 time units on R and must start after P finishes. Both tasks are non-preemptive. Minimize Q's finish time. In your final answer, show a two-row timetable (task, resource, start, finish), verify both durations and the precedence/non-overlap inequality, and prove optimality with the P-to-Q chain lower bound. Use only the given facts and ordinary arithmetic. Do not create or modify files, write scripts, build software, start a server or use the internet.

Solve an operations-research scheduling problem. Deliver the answer directly as a planning analysis in your final response: a timetable, feasibility checks and an optimality proof. Do not create or modify any files, write a script, build an application, start a server or access the internet. The work product is reasoning, not software or a generated document. The workshop has two resources M1 and M2; each can perform at most one task at a time. Time starts at zero. Tasks are non-preemptive and cannot start before all predecessors finish: A: duration 2, resource M1, no predecessor. B: duration 3, resource M2, predecessor A. C: duration 2, resource M1, predecessor A. D: duration 2, resource M1, predecessors B and C. E: duration 1, resource M2, predecessor D. Minimize the finish time of E. Show an explicit table with task, resource, start and finish. Check each task duration, every precedence edge and resource non-overlap with numerical inequalities. Give a lower-bound proof from a precedence chain and show the schedule attains it. Distinguish the proof of optimality from merely finding a feasible schedule. Keep the response self-contained.