The Night-Shift Bakery and the Vanishing Ovens
A neighborhood bakery runs two ovens. The large oven produces 240 loaves per night; the small oven produces 90. During a heat wave, the large oven is shut down for repairs on Tuesday and Thursday, and the small oven runs at 60% capacity on those same nights because the shop's breaker trips. On all other nights both ovens run normally. The owner needs to deliver 1,500 loaves over a seven-day week (Monday through Sunday) to fulfill a contract. She has already delivered 620 loaves by the end of Monday. She tells her partner, "We'll be fine as long as the small oven never drops below half its usual output."
1. Using only the numbers in the setup, determine whether the owner's claim that the week's 1,500-loaf contract can be met is correct.
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Compute total capacity for the week. Normal nights (Mon, Wed, Fri, Sat, Sun = 5 nights): 240 + 90 = 330 per night, so 5 × 330 = 1,650. Repair nights (Tue, Thu = 2 nights): large oven is off (0), small runs at 60% of 90 = 54 per night, so 2 × 54 = 108. Total weekly capacity = 1,650 + 108 = 1,758. The contract is 1,500, so capacity exceeds need by 258 loaves. However, the owner's stated condition - small oven never below half its usual output - is satisfied on repair nights (54 > 45), but that condition is not what determines success. Even if the small oven dropped to 45 on repair nights, capacity would be 1,650 + 90 = 1,740, still above 1,500. The claim "we'll be fine" happens to be true, but the stated reason is irrelevant to the arithmetic. The real constraint is the large oven's shutdown, which costs 2 × 240 = 480 loaves of capacity. The correct judgment: the contract can be met, but the owner's reasoning misidentifies the limiting factor.
2. The partner points out that by the end of Monday only 620 loaves were delivered, not 330. Does this change the weekly feasibility conclusion?
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The 620 figure is a cumulative delivery count, not a capacity figure. If 620 were delivered on Monday alone, that already exceeds the 330 single-night capacity, which is impossible given the stated oven outputs - so 620 must include prior backlog or a different accounting. Either way, feasibility is judged against remaining need, not against a single day's output. Remaining need after Monday = 1,500 − 620 = 880. Remaining capacity for Tue–Sun = (Tue 54) + (Wed 330) + (Thu 54) + (Fri 330) + (Sat 330) + (Sun 330) = 1,428. Since 1,428 > 880, the week remains feasible with a margin of 548. The key reasoning move is to separate cumulative delivered totals from per-night capacity and to recompute against the remaining days rather than the full week.