Chicken Order for a Saturday Pickup
A church kitchen must prepare 220 servings of baked chicken for a Saturday 11:30 a.m. pickup. The standard recipe yields 30 servings and calls for 4.5 pounds of chicken thighs at $3.20 per pound. Only whole batches are cooked, and the kitchen serves every batch it makes. The walk-in cooler holds 34 pounds of thighs. One oven holds three pans, each pan bakes one batch, and each load takes 40 minutes; prep before the first load takes 15 minutes, and pans can be reloaded the moment a load comes out. Two volunteers arrive at 8:00 a.m.
1. How many batches should the kitchen make, how much chicken is that, and does the cooler hold enough?
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Step 1 - Batches needed 220 ÷ 30 = 7.33 batches. Since only whole batches are cooked, round up to 8.
Step 2 - Servings produced 8 × 30 = 240 servings, which covers the order with 20 extra.
Step 3 - Chicken required 8 × 4.5 = 36 pounds. Cost: 36 × $3.20 = $115.20.
Step 4 - Compare to the cooler The cooler holds 34 pounds; 36 − 34 = 2 pounds short (worth $6.40). Someone must buy at least 2 more pounds before Saturday.
Why rounding down fails: 7 batches yield 210 servings, 10 short of the order. Saving $14.40 of chicken while missing the pickup is a bad trade, so 8 batches is the minimum acceptable plan.
2. Using the oven schedule, when will the last pan come out, and how much slack is there before the 11:30 pickup?
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Step 1 - Loads required The oven holds 3 pans and each pan is one batch. For 8 batches: 3 + 3 + 2 = 3 loads (the last load runs partly empty).
Step 2 - Baking time 3 loads × 40 minutes = 120 minutes.
Step 3 - Add prep Prep 15 minutes + 120 minutes = 135 minutes = 2 hours 15 minutes.
Step 4 - Clock time Start 8:00 a.m. → first load in at 8:15 → loads end at 8:55, 9:35, and 10:15.
Slack: 10:15 to 11:30 is 1 hour 15 minutes for cooling, panning, and transport.
Judgment note: the schedule works, but it assumes reloading happens instantly and no volunteer takes a break mid-load. If the kitchen wants a cushion, starting prep at 8:00 sharp is mandatory rather than optional.
3. A volunteer suggests making 7 batches to save money. Evaluate that proposal using the numbers, and name one other constraint the kitchen should check before Saturday.
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The proposal's arithmetic 7 batches × 30 = 210 servings - 10 short of the 220 ordered. Chicken saved: 4.5 lb × $3.20 = $14.40. Oven loads: still 3 (3 + 3 + 1), so it saves no baking time either.
Verdict: reject it. The kitchen gives up $14.40 and fails the order, and the pickup cannot be patched with partial servings once the food is plated.
Constraints worth checking
- Refrigeration: the cooler is already 2 pounds short, so storage for the extra 20 servings of finished chicken also needs confirming.
- Pans and racks: 8 pans must exist and fit three at a time.
- Transport: 240 servings need containers and a vehicle, a cost the chicken price does not include.
Each of these can break the plan even though the batch math is correct.