The 9:45 Pickup
A copy center must produce 5,000 printed sheets before a customer's 9:45 a.m. pickup. Two presses are available starting at 9:00 a.m. Press A runs at 60 sheets per minute and can start immediately. Press B runs at 40 sheets per minute but needs a 10-minute warm-up before it produces any sheets; warm-up begins at 9:00. Neither press can be sped up and no other equipment is free. If Press B jams, it stops instantly and cannot be restarted before the pickup; Press A is unaffected. The operator must decide now whether to promise the customer the 9:45 time.
1. If nothing jams, at what time does the job finish? Show the arithmetic.
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Split the run into two phases.
Phase 1, 9:00–9:10: Press A alone. 60 sheets/min × 10 min = 600 sheets. Remaining: 5,000 − 600 = 4,400 sheets.
Phase 2, from 9:10: A + B together. 60 + 40 = 100 sheets/min. 4,400 ÷ 100 = 44 minutes.
9:10 + 44 min = 9:54 a.m.
Check: 600 + (44 × 100) = 600 + 4,400 = 5,000. ✓
2. Can the 9:45 deadline be met? If not, by how many sheets does the job fall short at that moment?
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No. Work backward from 9:45.
From 9:10 to 9:45 is 35 minutes of combined running. 600 + (35 × 100) = 600 + 3,500 = 4,100 sheets.
Shortfall: 5,000 − 4,100 = 900 sheets, i.e. 9 minutes of combined output.
What to tell the customer: the earliest honest promise is 9:54 a.m. Any promise of 9:45 requires 900 more sheets in the same window, which neither press can deliver.
3. Press B jams at 9:30. When does the job finish, and what is the best use of the remaining time?
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Output at the jam: 600 (phase 1) + 20 min × 100 = 600 + 2,000 = 2,600 sheets. Remaining: 5,000 − 2,600 = 2,400 sheets, now at Press A's 60/min. 2,400 ÷ 60 = 40 minutes. 9:30 + 40 min = 10:10 a.m.
Judgement: with 20 minutes of B's output lost, no reallocation saves the deadline - A is already at capacity, so the only lever is communication. Tell the customer at 9:30 (not 9:45) that the run will be complete at 10:10, and offer partial delivery of the 2,600 finished sheets at 9:45 if the customer can use them.