Project ForgeA batch reactor produces 1×10⁵ kg of a product per year. The total batch time (in hours) of the reactor is k√PB, where PB is the product per batch in kg and k=1.0 h/√kg. The operating cost of the reactor is Rs. 200/h. The total annual fixed charges are Rs. 340×PB and the annual raw material cost is Rs. 2×10⁶. The optimum size (in kg) of each batch (adjusted to the nearest integer) is
- A748
- B873
- 953
- D1148
Explanation
Batches per year=1×10⁵/PB; annual operating cost=200×(1×10⁵/PB)×√PB=2×10⁷/√PB. Total variable cost (excluding fixed raw material cost) C(PB)=2×10⁷·PB^(−0.5)+340PB. dC/dPB=−10⁷·PB^(−1.5)+340=0 ⟹ PB^1.5=10⁷/340=29412 ⟹ PB=29412^(2/3)≈953 kg.
Source: GATE CH 2012 (2012)
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